Smart Sonic bearings for frictional force reduction and switching

ABSTRACT

An ultrastiff precision sonic bearing assembly and method thereof for controlling an effective coefficient of friction between two elements in slidable contact configured along an interface under a force sufficient to maintain contact and having static friction therebetween, by inducing a repetitive motion in one of the elements parallel to the interface thereby altering the effective coefficient of friction therebetween. The bearing assembly also provides for additional and independent electronic control over the average thickness thereof and senses the force thereon to allow the bearing assembly stiffness to be altered.

BACKGROUND FIELD OF THE INVENTION

[0001] This invention relates to plain bearing-like devices and moreparticularly to precision, ultrastiff plain bearing-like structures bothmacroscopic and microscopic with frictional and structural propertiesthat can be electronically controlled and which contain a built-inultrastiff force sensing mechanism.

[0002] Precision bearings, specifically designed to translate or rotatea mechanical load with submicron accuracy have become increasinglyimportant in the optics, semiconductor manufacturing, and micromachiningindustries. Unlike regular bearings that are used, for example inautomobiles, these precision bearings have unique primary and secondarycharacteristics. Among the most important primary characteristics are(1) extremely high stiffness, (2) controllable frictionalcharacteristics, (3) enhanced smoothness-of-travel, and (4) superioraccuracy-of-travel. Some of the secondary features are (a) high damagethreshold, (b) high reliability, (c) low maintenance, (d) low externalsupport requirements, and of course (e) low cost.

[0003] A common bearing, found in many semi-precision, mechanisms, isthe sliding bearing or plain bearing which coincidentally also exhibitsmany of the primary and secondary characteristics of a precisionbearing. As used herein, the term “plain bearing” simply means that thebearing's load is supported through sliding motion between two solidsurfaces. FIG. 1A illustrates a lubricated planar configuration of asimple plain bearing, which consists of a flat bar-shaped upperslide-plate 50 and a similar lower slide-plate 54 sliding against eachother with a lubricant 52, such as oil, between the sliding surfaces.FIG. 1B shows two forces acting on the upper slide-plate of the simpleplain bearing of FIG. 1A. The force, F_(APP) 45, is an applied forcesufficient to maintain contact along an interface between the surfacesof the two slide-plates. The other force is an applied sliding force 46,which, along with the component of the force 45 parallel to theinterface, can be used to translate the two slide-plates relative toeach other.

[0004] A plain bearing is characterized by (1) its inherent simplicity,having a minimum number of moving parts; (2) its superior runout oroff-axis error characteristic which is obtained by averaging any localsmoothness imperfections over the entire sliding surface area; (3) itshigh shock-loading or damage threshold which is the result of spreadingthe shock force on the bearing over a large surface area, and (4) itsextremely high compressive stiffness since the bearing has large directmaterial to material sliding contacts.

[0005] However, despite all of these advantages, a lubricated plainbearing is not generally used in precision applications for severalreasons. The first reason is because of the bearing's relatively highfrictional forces generated by the component [F_(APP)]_(Z) of the force45 which is perpendicular to the interface . These frictional forces area direct result of its high coefficient of friction, which can be ten toone hundred times larger than an equivalent ball or air bearing. Thesecond reason is because of stiction, an extra frictional holdingphenomenon, above the “normal” static friction, that occurs when twoextremely smooth and lubricated contacting surfaces that werestationary, start to slide. The third reason is because of a phenomenonknown as stick-slip which results in fluctuations in the frictionalforces while the bearing is in motion. The cumulative effects from allthree phenomena associated with a plain bearing, will usually render aninstrument equipped with this type of bearing unable to perform preciseand microscopic movements.

[0006] In prior art, there are three general methods used to change thefrictional forces between two sliding surfaces. First, the actualcoefficient of friction between the sliding surfaces can be modified byvery thin films or coatings with good tribological properties. This isgenerally accomplished by using some combination of a solid, liquid orgas as reviewed in U.S. Pat. No.4,944,606 of Lindsey et al., (1990) andU.S. Pat. No. 5,911,514 of Davies et al., (1999). Second, if one or moreoperating parameters between the two sliding surfaces can be altered,the frictional characteristics can be changed. Some common operatingparameters that can be readily controlled to produce a relatively smallvariation in frictional behavior are surface temperature, as describedin U.S. Pat. No. 5,441,305 of Tabar (1995) and sliding speed, as shownin U.S. Pat. No. 5,043,621 issued to Culp (1991). Finally, if thecompressive force between the two sliding surfaces is minimized, ortime-modulated as revealed in U.S. Pat. No. 3,774,923 of Suroff (1973) ,U.S. Pat. No. 3,756,105 of Balamuth et al., (1973), and U.S. Pat. No.4,334,602 of Armour et al., (1982), or even totally eliminated by, forexample, magnetic levitation as shown in U.S. Pat. No.3,937,148 issuedto Simpson (1976), then the frictional force generated between these twosurfaces is correspondingly minimized.

[0007] All these techniques of friction reduction can be usedindividually or possibly, in some cases, in combination. Examples areair bearings, like those described in U.S. Pat. No. 3,683,476 of Lea etal., (1972), used in precision translational stages where a combinationof an air film and levitation techniques are employed to reducefriction.

[0008] Solutions to the stiction phenomenon were revealed inapplications related to magnetic disk storage. U.S. Pat. No. 4,530,021issued to Cameron (1985) and U.S. Pat. No. 6,002,549 issued to Berman etal., (1999), teach that vibrational techniques, which dither the sliderhead also free it from the force of stiction. Further solutions to thestiction problem involve surface texturing techniques, as illustrated byU.S. Pat. No. 5,079,657 of Aronoff et al.,(1991), which allow a sliderhead to leave a surface smoothly.

[0009] Similarly, the stick-slip problem has also been successfullyaddressed in diverse fields, such as those including focusing mechanismsused in optical disk storage and wiping mechanisms for automotivewindshields. Their solutions, like the stiction case, are also basedupon oscillation methods as revealed in U.S. Pat. No. 4,866,690 issuedto Tamura et al., (1989) and U.S. Pat. No. 5,070,571 issued to Masuru(1991).

[0010] However, all these prior art techniques suffer from one or moredrawbacks which render their benefits, in a plain bearing-like deviceapplication, individually insufficient and in some cases, incompatiblewith precision. For example, simply adding a lubricant between the twosurfaces of a plain bearing does not minimize either stiction orstick-slip behavior which are required for smooth microscopic motion aswell as positioning accuracy. Controlling the aforementioned operatingparameters does not reduce the coefficient of friction enough for mostapplications. Changing the compressive force by periodic or continuouslevitation compromises bearing compressive stiffness, produces changesin the bearing position depending upon whether the bearing is levitatedor not, and may require substantial external facility support such as,in the case of air bearings, a continuous supply of clean, dry airdelivered at a regulated pressure. Furthermore, U.S. Pat. No. 4,648,725of Takahashi (1987), teaches that positioning devices employing bearingswith only a fixed, very low coefficient of friction, such as an airbearing, tend to have an extended settling time even after moving atrelatively low velocity to a particular position of interest.

[0011] Also, prior art examples using vibrational or oscillationtechniques to minimize stiction or stick-slip make no effort to separatethe vibrational motion from the ideally desired motion of the load.Separation of the two motions is paramount in precision bearings wheremaintaining the integrity of the slidable path, continuously contactingsurfaces, and vibrational insensitivity are all desired properties.Furthermore, prior techniques that use the vibrational motion only priorto moving the load along its desired path do not remove any stick-slipproblem from occurring during travel.

[0012] Therefore, in order for any plain bearing-like devices to besuccessfully employed for precision and microscopic movementapplications, simultaneous solutions to the high friction, shortsettling time, stiction, and stick-slip issues must be implementedutilizing techniques obtained from many different technical areas.

[0013] Furthermore, in order to utilize such a plain bearing-like deviceas “real” ultrastiff bearing, an important additional bearingcharacteristic must be addressed. In prior art, when bearings areincorporated into a stage for example, there is generally anincompatibility between the ultrastiff requirement and the bearing'smechanical tolerances. Ideally, for a stage to be truly ultrastiff inone or more axes orthogonal to the direction of travel, all thecomponents of the stage must have essentially zero mechanical toleranceor “play” in these orthogonal directions. In prior art, the solutions tothis problem are (1) to simply minimize these mechanical tolerances bymanufacturing mechanical components to nearly exact specifications, or(2) to compensate for the mechanical variations by incorporating elasticmembers between moving surfaces, or (3) to maintain an equivalent “zerotolerance” condition by dynamically adjusting one or more mechanicalcomponents. Of these heretofore mentioned solutions, only the activelyservoed technique of dynamic compensation approaches the idealmechanical stiffness requirements and this dynamic adjustment techniquehas been successfully implemented in the form of an air bearings, likethose described in U.S. Pat. No. 3,683,476 of Lea et al., (1972).Therefore, for success in ultrastiff applications, a plain bearing-likedevice must also contain a solution to this incompatibility betweenmechanical tolerance and stiffness.

[0014] To complete the prior art survey, a seemingly unrelated deviceknown as the ultrasonic bonder should also be included.

[0015] The ultrasonic bonder or wire bonder is commonly used in thesemiconductor industry to electrically connect the integrated circuitchip to the leadframe pins. Ultrasonic bonding, also known as welding orfriction-fusion bonding, is a process for joining two materials by meansof a bonding tool which exerts a normally directed clamping, mashing, orapplied force on two juxtaposed contacting surface areas while vibratingone parallel to the other at an ultrasonic frequency. As a result, localplastic deformation takes place in the interfacing materials and ametallurgical bond is formed between the two materials. The originalthermosonic bonder, as described in U.S. Pat. No. 3,054,309 of Elmore(1962), and its many descendants, typified by U.S. Pat. No.5,186,378issued to Alfaro (1993), generally requires not only a clamping ormashing pressure (around 200 MPa) and ultrasonic vibrations (around 60kHz) but also high temperatures (around 175° C. to 300° C.) to obtainnear 100 percent intermetallic coverage. Recent advances include anambient temperature (around 27° C.) ultrasonic wire bonder, as revealedin U.S. Pat. No. 5,244,140 of Ramsey et al., (1993), and a thermoplasticwelding apparatus described in U.S. Pat. No. 4,482,421 issued to Gurak(1984).

SUMMARY OF THE INVENTION

[0016] An ultrastiff precision sonic bearing assembly and method thereoffor controlling an effective coefficient of friction between twoelements in slidable contact configured along an interface under a forcesufficient to maintain contact and having static friction therebetween,by inducing a sinusoidal oscillatory sliding motion in one of theelements parallel to the interface thereby altering the effectivecoefficient of friction therebetween. The bearing assembly also providesfor additional and independent electronic control over the averagethickness thereof and senses the component of the force perpendicular tothe interface thereon.

[0017] A simple implementation of this method is in a planar form of alinear sonic bearing, comprising of a moveable load member having a loadsliding surface for translating along any slidable path direction on abearing element's bearing sliding surface. A lower stationary basemember supports both the bearing element and the load member. Thebearing element resonates in response to an applied energizing meanswhich reduces the effective coefficient of friction μ_(SB) between theload and the bearing sliding surfaces. The effective coefficient offriction can be smoothly and rapidly changed by controlling theamplitude of the oscillatory sliding motion. The effective static anddynamic stiffness of the sonic bearing can also be independently andsmoothly controlled by applying a bias to the bearing element whichmodulates the thickness of the bearing element. Applications of theinvention can be found in such devices as ultrastiff, precision bearingsand sensors.

[0018] The primary steps used to optimally achieve the apparentfrictional reduction are to: (a) preselect the surface materials for thecontacting surfaces to minimize ultrasonic induced bonding, (b)pre-texture the contacting surfaces to minimize stiction, (c) pre-coatthe contacting surfaces with a film to reduce the actual coefficient offriction and to serve as an anti-bonding agent, and (d) induce into thebearing sliding surface, a sinusoidal oscillatory sliding motion whoseresulting frictional forces are balanced and whose oscillation level canbe controlled. Furthermore, in order to provide ultrastiffness, eachslidable contact between bearing components should be a direct materialto material contact with large surface area so that the inherent bearingstiffness is determined primarily by the material compressibility. Toenhance this ultrastiff aspect of the invention, the thickness of one ormore components in the bearing assembly can be altered in response to avariation in the force in order to provide an additional stiffness servomechanism by: (a) preselecting the material in a portion of the bearingassembly subject to the same force as the sliding surfaces to haveelectromechanical properties which facilitate the desired dimensionalchange, (b) sensing the magnitude of the normal component of the forceon the bearing element to determine the value of a high voltage signal,and (c) applying that high voltage signal to that portion of the bearingassembly in such a manner as to maintain a constant perpendicularcomponent of the force by producing the desired dimensional change.

[0019] It is accordingly a primary object of the present invention toprovide a sonic bearing assembly that retains all the desirableproperties of a plain-type bearing such as high compressive stiffness,low sensitivity to shock-loading, and minimal off-axis error whilemaintaining a very low effective coefficient of friction μ_(SB).

[0020] It is accordingly another primary objective of the presentinvention to provide an electronic controlling means which allows theeffective coefficient of friction of the bearing assembly to be easilyand rapidly changed between its high and low states. This characteristicenables a stage equipped with sonic bearings to minimize the settlingtime after the load has reached the designated coordinate whileminimizing positional error in one or more axes orthogonal to theslidable path.

[0021] It is accordingly a further primary objective of the presentinvention to provide an electronic controlling means for dimensionallyaltering one or more components in the bearing assembly to allow forattributes such as variable thickness, position modulation, temperaturecoefficient compensation, low frequency vibrational damping, damping ofvariations in compressive force, bearing wear compensation, andrelaxation of manufacturing and/or alignment tolerances while stillbeing able to achieve the equivalence of the “zero tolerance” criteriaas required for use in precision and ultrastiff instruments.

[0022] Furthermore, another primary object is to provide a sensing meansfor measuring the magnitude of the normal component of the force on thebearing assembly so that a signal representing that magnitude can beprovided for use in a feedback mechanism to enhance the stiffness of thesonic bearing assembly.

[0023] It is another object of the present invention to provide abearing assembly that exhibits minimal stiction and stick-slipproperties which, in combination, will improve the ability of a stageusing sonic bearings to move a load with increased smoothness andprecision.

[0024] A further object of the present invention is to provide a bearingassembly which maintains its high effective coefficient of frictionμ_(SB) with or without using any electrical energy. This characteristicenables a stage equipped with sonic bearings to “lock” its position.

[0025] A still further object of the present invention to providebearings with high reliability by using only solid state components withvery few moving parts.

[0026] An additional object of the invention is to provide bearings withdiversified geometries which can accommodate application specificrequirements such as microscopic dimensions, or translational,rotational, or multi-axial movements.

[0027] Furthermore, according to one aspect of the present invention,another object is to provide bearings with wear resistance, hence longoperational life, by using extremely hard, laminated, or customizedmaterials, or any combination thereof as the sliding surfaces withsurface treatments including ion implantation.

[0028] In other preferred forms of the present invention, the bearingcan be operated in environments with harsh conditions which may includehigh vacuum, cryogenic temperatures, ionizing radiation, corrosivevapor, high magnetic fields or any combination thereof.

[0029] Further objects and advantages are to capitalize on existingoptical polishing and quality control technologies used to manufacturehigh precision surfaces for very hard materials at low costs. Stillfurther objects and advantages will become apparent from considerationsof the ensuing descriptions and drawings.

DRAWING FIGURES

[0030]FIG. 1A is an isometric view of a prior art lubricated plainbearing having planar geometry.

[0031]FIG. 1B is a side view of a prior art lubricated plain bearinghaving planar geometry with forces.

[0032]FIG. 2A is an isometric view of a piezoelectric transduceroscillating at its fundamental longitudinal frequency and subjected tothe free-free boundary conditions.

[0033]FIG. 2B is a plot of a piezoelectric transducer's surfaceoscillation velocity in the Y direction as a function along its lengthwhich is aligned in the Y direction and subjected to free-free boundaryconditions.

[0034]FIG. 3A is an isometric view of a two component direct-drive sonicbearing design comprising of a piezoelectric bearing element secured toa stationary external platform and supporting a load on a load member.

[0035]FIG. 3B is an isometric view of a two component indirect-drivesonic bearing design comprising of a composite bearing element having apiezoelectric transducer and an extension member secured to a stationaryexternal platform and supporting a load on a load member.

[0036]FIG. 4A is an isometric view of an ultrastiff direct-drive sonicbearing element comprising of a single, fundamental, longitudinal lengthresonant mode piezoelectric transducer equipped with contact padmembers.

[0037]FIG. 4B is an isometric view of an ultrastiff direct-drive sonicbearing element comprising of a single, fundamental, longitudinal lengthresonant mode, laminated magnetostrictive transducer equipped withcontact pad members.

[0038]FIG. 4C is an isometric view of an ultrastiff direct-drive sonicbearing element comprising of a vertically stacked piezoelectrictransducer equipped with contact pad members.

[0039]FIG. 4D is an isometric view of an ultrastiff direct-drive sonicbearing element comprising several piezoelectric transducershorizontally stacked in succession where the bearing element is equippedwith contact pad members.

[0040]FIG. 5A is an isometric view of an ultrastiff indirect-drive sonicbearing element comprising of a single, fundamental, length resonantmode, piezoelectric transducer driving a single, fundamental,longitudinal length resonant mode, extension member.

[0041]FIG. 5B is an isometric view of an ultrastiff indirect-drive sonicbearing element consisting of a single, fundamental, length resonantmode, magnetostrictive transducer driving a single, fundamental,longitudinal length resonant mode, extension member.

[0042]FIG. 5C is an isometric view of an ultrastiff indirect-drive sonicbearing element using two, fundamental, longitudinal length resonantmode, piezoelectric transducers driving a single, fundamentallongitudinal length resonant mode, extension member.

[0043]FIG. 5D is an isometric view of an ultrastiff indirect-drive sonicbearing element using four piezoelectric transducers driving a squareextension member.

[0044]FIG. 5E is an isometric view of an ultrastiff indirect-drive sonicbearing element using a single piezoelectric transducer driving twoidentical stepped horn extension members.

[0045]FIG. 6A is an exploded view of a simple ultrastiff linear sonicbearing assembly employing a direct-drive sonic bearing element,sandwiched between a load member and a base member.

[0046]FIG. 6B is an exploded view of a simple ultrastiff linear sonicbearing assembly using a direct-drive sonic bearing element with anupper and lower lubricant reservoir.

[0047]FIG. 7A is a simplified block diagram of an electronics packagedriving one ultrastiff bearing element.

[0048]FIG. 7B is a simplified block diagram of an electronics packageconfiguration for driving an ultrastiff bearing element having twopiezoelectric transducers.

[0049]FIGS. 8A to 8C are side views of an ultrastiff direct-drive sonicbearing element oscillating at its fundamental longitudinal frequencyand subjected to the free-free boundary conditions illustrating theextremes of thickness modulation along the length due only to theresonant oscillation.

[0050]FIGS. 8D to 8F are side views of an ultrastiff direct-drive sonicbearing element oscillating at its fundamental longitudinal frequencyand subjected to the free-free boundary conditions illustrating theextremes of thickness modulation along the length due to oscillation andan independent increase in thickness due to an applied high voltage.

[0051]FIG. 9A is an isometric view of an ultrastiff indirect-drive sonicbearing element consisting of a single, fundamental, length resonantmode, piezoelectric transducer driving a single, two-half wavelength,longitudinal length resonant mode, extension member which is also apiezoelectric transducer, both connected to a single electronicspackage.

[0052]FIG. 9B is an isometric view of an ultrastiff direct-drive sonicbearing element consisting of a single piezoelectric transducersupported by a base member which is also a piezoelectric transducer,both connected to a single electronics package.

[0053]FIG. 10 is a side view of a simplified ultrastiff direct-drive,sonic bearing assembly with the associated forces acting on it and withconnections to an electronics package.

[0054]FIG. 11A is an experimental plot of the effective coefficient offriction μ_(SB) of a sonic bearing with tungsten carbide contact padsurfaces versus the root-mean-square (r.m.s.) velocity ν_(SB) ^(rms) ofits contact pad surfaces.

[0055]FIG. 11B is an experimental plot of the actual coefficient ofkinetic friction of a cleaned and polished tungsten carbide rod slidingagainst a tungsten carbide plate as a function of its linear slidingvelocity ν.

[0056]FIG. 12A is an experimental plot of the external r.m.s. load powerdissipation due to frictional sliding of a sonic bearing versus ther.m.s. velocity ν_(SB) ^(rms) of its contact pad surfaces.

[0057]FIG. 12B is an experimental plot of the internal r.m.s. powerdissipation of a piezoelectric transducer in a sonic bearing elementversus the r.m.s. velocity ν_(SB) ^(rms) of the contact pad surfaces.

[0058]FIG. 13A is an experimental setup used to measure the dependenceof the effective coefficient of friction μ_(SB) for an ultrastiff sonicbearing on the path of sliding as referenced against the axis of bearingelement oscillation.

[0059]FIG. 13B is an experimental plot of the effective coefficient offriction μ_(SB) of an ultrastiff sonic bearing versus the sliding pathangle θ of the bearing in the active (ON) and inactive (OFF) states.

[0060]FIG. 14A is an experimental setup used to identify therelationship between the normal component [F_(APP)]_(Z) of the force ona bearing element and the value of the force output signal.

[0061]FIG. 14B is an experimental plot of the normal component[F_(APP)]_(Z) of the force on the bearing element versus the forceoutput signal.

[0062]FIG. 15A is an isometric view of a simplified long lengthultrastiff sonic bearing using a three-half wavelength, longitudinallength resonant mode direct-drive bearing element along with theelectronics package for driving it.

[0063]FIG. 15B is an isometric view of a simplified long lengthultrastiff direct-drive sonic bearing having a bearing element withthree, one-half wavelength, longitudinal length resonant mode transducerelectrode segments in succession, each segment having alternatingelectric field polarity.

[0064]FIG. 15C is an isometric view of a simplified long length,ultrastiff indirect-drive sonic bearing using a one-half wavelength,longitudinal length resonant mode transducer coupled to a three-halfwavelength, longitudinal length resonant mode, extension member havingthe same resonant frequency.

[0065]FIG. 16 is an isometric view of a simplified ultrastiff sonicbearing example equipped with upper contact pad members that havecylindrically concave contact pad surfaces to support a rod-likecylindrical load member.

[0066] FIGS. 17 to 19 each show an isometric view of a simplified,multi-bearing element, sonic bearing assembly employing a pair ofopposing ultrastiff direct-drive bearing elements sandwiching a loadmember with different force servo mechanism configurations betweenbearing elements.

[0067] FIGS. 20 to 22 show isometric views of the sonic bearing assemblyconfiguration of FIG. 17 illustrating the effect of the force feedbackfor the case when the load member undergoes a dimensional change.

[0068]FIG. 23A is a plot showing the change in the upper bearing elementthickness ΔZ_(BE2) as a result of changing the applied adjustable highvoltage V_(HV2) in order to maintain a constant force [F_(APP)]_(Z) onthe lower bearing element for each of the states described in FIGS. 20to 22.

[0069]FIG. 23B is a plot showing the change in the upper bearing elementgenerated force [F_(BE2)]_(Z) as a result of changing the appliedadjustable high voltage V_(HV2) in order to maintain a constant force[F_(APP)]_(Z) on the lower bearing element when a unidirectionalexternal force [F_(EXT)]_(Z) is applied to the lower bearing element forthe sonic bearing assembly configuration of FIG. 17.

[0070]FIGS. 24A to 24C graphically illustrate the relationship of thestiffness of the sonic bearing assembly configuration of FIG. 17 with anexternal force [F_(EXT)]_(Z) of arbitrary magnitude is applied to it.

[0071]FIGS. 25A to 25C graphically illustrate the relationship of thestiffness of the sonic bearing assembly configuration of FIG. 18 with anexternal force [F_(EXT)]_(Z) of arbitrary magnitude is applied to it.

[0072]FIGS. 26A to 26C graphically illustrate the relationship of howthe stiffness of the sonic bearing assembly configuration of FIG. 19 ismaintained when an external force [F_(EXT)]_(Z) of arbitrary magnitudeis applied to it.

[0073]FIG. 27 contains an isometric view of a simplified multi-bearingelement sonic bearing assembly employing two pairs of opposingultrastiff direct-drive bearing elements and also shows an externalconfiguration for the drive electronics package of each bearing elementin one opposing pair.

DETAILED DESCRIPTION OF THE INVENTION

[0074] One of the fundamental objectives of all friction reductiondevices is to minimize the applied sliding force necessary to initiateand sustain a sliding motion between the contacting surfaces of twoobjects. In prior techniques, such as those that use lubricants, balls,or variations in operating parameters, this goal was achieved byactually reducing the actual coefficients of friction. Other priormethods, such as magnetic and vibrational levitation techniques, do notreduce the coefficients of friction itself, but minimize the compressiveor normal component of the force between the two sliding surfaces whichin turn, will minimize the required applied sliding force.

[0075] The present invention uses a different approach to reach the samegoal by externally supplying most of the energy that is dissipated bythe frictional sliding process in a manner that does not, on theaverage, interfere with the original load sliding motion. If thistechnique is implemented on two sliding surfaces, there will be anapparent reduction of the coefficient of friction, hereinafter referredto as a reduction in the “effective coefficient of friction” μ_(SB),since the energy drain normally associated with frictional sliding isnow primarily supplied by an independent source, and only secondarilyfrom the kinetic energy of the moving load itself. The sliding loadwill, for the most part, maintain its original velocity and thereforehave the appearance of sliding on a surface with very low friction. Thisreduction of the effective coefficient of friction is achieved in amechanical structure called a sonic bearing.

[0076] In its most simplistic form, the adhesion theory of frictionindicates that for very hard and very smooth surfaces, sliding frictionis the result of energy losses from the severing of chemical bondsbetween the tips of microscopic asperities (i.e., high peaks) at theinterface of two sliding surfaces. Specifically, the severing ofchemical bonds occurs when the asperities that are constantly beingformed to connect the two surfaces, are non-elastically or plasticallydeformed and sheared. In a normal sliding process, the energiesdissipated by the frictional forces are usually extracted from thekinetic energy of the sliding load itself, hence as an unaided loadslides along a level frictional surface, it slows and eventually stops.Hereinafter, the motion of a load sliding on a surface will be referredto as the load sliding motion.

[0077] Therefore, without imposing any limitations on the scope of theclaims, we propose that the friction reduction aspect of the inventionis based upon the following concepts: (1) most of the bond deforming andshearing energy due to friction can be supplied by an external sourcerather than by extracting it from the kinetic energy of the sliding loaditself; (2) the external energy can be supplied via techniques that donot significantly interfere with the original load sliding motion; (3)the sliding surfaces' material properties and surface properties can beselected to inhibit the bonding of these surfaces due to the abruptrelease of stored chemical energy associated with the bond's nonelasticdeformation and shearing; and (4) severance of the bond releases theload to move in any path that is slidable. Assuming that these conceptsare valid and appropriate hardware implemented, then the kinetic energyof the unaided sliding load will be held nearly constant during slidingand the moving load will slow down only very gradually. We havetherefore obtained very low effective coefficient of friction betweenthe two sliding surfaces, even though the actual coefficient of frictionbetween these surfaces can be relatively large and remain unaltered.

[0078] The basic principles of the adhesion theory of friction, alsoknown as the Adhesion, Junction-growth, and Shear (AJS) model, are wellknown in the art and are described in detail in the literature. See forexample, Ludema, K. C., “Friction, Wear, Lubrication”, CRC Press, BocaRaton, New York, 1996, pp. 72-81 and Blau, P. J., “Friction Science andTechnology”, Mercel Dekker, New York, 1995, pp. 138-147.

PREFERRED EMBODIMENTS

[0079] In the preferred embodiment of the invention, a load memberhaving a load sliding surface is sliding on a bearing element having abearing sliding surface, where the asperities at the interface arerepetitively deformed and sheared to allow the load member to slide in aload sliding motion when acted on by an applied sliding force. Anenergizing means is used for inducing a symmetrical, oscillatory slidingmotion into the bearing element by way of a transducer, and thisoscillatory sliding motion is totally separate from any load slidingmotion of the load member. The main characteristics of this oscillatorysliding motion are that: (1) the root-mean-square (r.m.s.) velocityν_(SB) ^(rms) of this motion is substantially larger than thetranslational speed of the load sliding motion ν_(LOAD); (2) thedirection of this motion is along any slidable path associated with theload sliding motion, but not necessarily along the same slidable path asthe load sliding motion; and (3) the distance versus time profile of anyone point on the bearing sliding surface from its equilibrium positionis substantially the same for each one-half cycle of the oscillation.

[0080] A simple and efficient method of inducing the requiredoscillatory sliding motion with all the heretofore mentionedcharacteristics into a bearing sliding surface is to produce alongitudinal resonance in a solid, substantially rigid elastic objectthat has the bearing sliding surface. This resonance can be achieved bydriving the transducer at one of its longitudinal resonant frequenciesand coupling the resulting acoustic resonant waves constructivelythroughout the body of that object. In this way, the transducer motionis amplified, by a factor proportional to the quality factor or Q of theresonance, relative to the non-resonant motion, for the same oscillatingtransducer input drive voltage.

[0081] The oscillatory sliding motion has a further requirement whichcomplements or is related to the topography of the load sliding surface.It is imperative that the load sliding surface topography does notchange the path of the oscillatory sliding motion in the bearingelement. Therefore, not only is the path of the oscillatory slidingmotion along any slidable path, but the motion itself must also notimpart a modulation to the force that holds the bearing sliding surfaceto the load sliding surface while interacting with the topography of theload sliding surface. The surface topographies may be of anyconfigurations, including planar, cylindrical, or spherical.

[0082] Additionally, one of the main tasks of the invention is to designa sonic bearing to minimize the side effects associated with theintroduction of this oscillatory sliding motion into the bearing slidingsurface. Generally, these effects can be grouped into two opposingcategories consisting of the motion-producing and the motion-inhibitingphenomena.

[0083] The motion-producing side effect is a phenomenon resulting fromthe transferring of the bearing sliding surface's oscillatory slidingmotion, via frictional forces, to the load sliding surface, resulting ina composite motion of the load member, consisting of the original loadsliding motion and the undesirable oscillatory sliding motion.

[0084] In the invention, three independent techniques are used to reducethis specific motion-producing side effect. The first, and of course themost obvious approach, is to directly reduce the oscillating frictionalforces on the load sliding surface generated by the oscillating bearingsliding surface. Traditionally, this is accomplished by employing alubricant, such as an oil film, between the two sliding surfaces. Morerecently however, a different approach based upon the adhesion theory offriction has been widely used. Basically, according to the theory, thecoefficient of friction between two hard sliding surfaces can besubstantially reduced if a softer intermediate solid film of a specificthickness is attached to one of the two hard surfaces. This reduction isachieved because the plastic deformation of the asperities between twosliding surfaces during sliding is limited only by the shear stress thatcan be sustained in the material of the soft surface film. Furthermore,this film can be modified by ion implantation to a predetermined numberof ions/cm² whereby the film is subjected to implantation of a depthgreater than the thickness of the film. This improves its wearcharacteristics without degrading the low actual coefficient offriction. This type of modification can be applied to any slidingsurfaces in the present invention, including but not limited to thesliding surfaces belonging to load members, bearing elements, extensionmembers, base members, contact pads, and load guideway members. Severalvery low friction designs using this technique are described in U.S.Pat. No. 4,824,262 issued to Kamigaito et al. (1989).

[0085] The second technique, called the temporally nulling method isbased upon the temporal symmetry of the induced motion on the loadsliding surface resulting from the symmetrical oscillatory slidingmotion of the bearing sliding surface. Specifically, any displacement ofthe load sliding surface in the time period of the first one-half cyclehas an equal and opposite displacement over the time period of thesecond one-half cycle. Thus, if the normal component of the forceF_(APP) between the load element and the bearing element is maintainedto be constant, and if the surfaces are adapted to have an actualcoefficient of friction substantially uniform along any slidable pathbetween the load member and the bearing element, then the netdisplacement of the load sliding surface will therefore be minimized bythe symmetry of the induced motion over a total time period of one fullcycle. An example of a symmetrical oscillatory sliding motion in anelastic material is a sinusoidal motion. This net displacement of theload sliding surface can be further reduced by attaching a substantiallylarge inertial mass to the load sliding surface to reduce the magnitudeof the aforementioned displacement in each one-half cycle.

[0086] The third technique, called the spatially nulling method ispredicated on the spatial symmetry of the oscillatory sliding motion ofthe bearing sliding surface. The general concept here is to mechanicallyarrange the bearing sliding surface to have two separate contactingregions or provide one contacting region on two different bearingsliding surfaces. Each region is designed to slide against the same loadsliding surface along an interface having a uniform coefficient offriction and both regions have an oscillatory sliding motion with thesame set frequency and similar set amplitudes. But each region has a setphase which is constantly 180 degrees out of phase from the other. Oncethese parameters are set, and the load member is configured to slideabout these regions of the bearing element, the effect of these twooscillating regions sliding against a common load sliding surface is tosimultaneously generate two substantially equal and opposite frictionalforces on that surface. The net result of these two frictional forces ona rigid load sliding surface is to substantially cancel any bearingelement induced movement on the load member at any given time. Theoptimum approach to minimizing this motion-producing side effect is, ofcourse, to utilize all three techniques simultaneously as is done in thepreferred embodiments of a sonic bearing.

[0087] Another very important side effect resulting from theintroduction of an oscillatory sliding motion into the bearing slidingsurface is the motion-inhibiting phenomenon. Basically, when two verysmooth surfaces are subjected to a combination of ultrasonicoscillations, force applied between the surfaces and elevatedtemperature, welding or bonding of the two sliding surfaces may occur.An important aspect in the design of a sonic bearing is, of course, toprevent this bonding phenomenon from occurring.

[0088] In the present invention, various methods are employed tominimize this motion-inhibiting side effect. In order to fully determinethe specific requirements for suppressing the motion-inhibiting sideeffect, it is instructive to review the bonding requirements of acommercially available ultrasonic bonder used in the semiconductorindustry. Bonding is optimized when: (a) the two contacting materialsused have the same crystalline structure, such as the case of Au and Al,which have face centered cube geometry; (b) the two melting pointtemperatures (e.g., Al is 660° C. and Au is 1064° C.) are less than ornear the ultrasonically induced, equivalent local surface temperaturerise of approximately 1000° C. (see F. Seits, Imperfection in NearlyPerfect Crystals, John Wiley, New York, 1952); (c) the contact pressurebetween the two surfaces is substantially high, like for the case of Aubonded to Al where it is approximately 200 MPa; (d) the ultrasonicfrequency is in the range of 60 to 200 kHz; (e) the ultrasonic power isin the range of 100 to 300 mW; (f) the average surface temperature is asclose to the materials' melting points as possible and for the case ofAu bonding to Al, the practical temperature range is from 175° to 300°C.; (g) the surfaces are free of foreign contaminates such as an oilfilm; and (h) the sonic energy application time for the case of Au wireon Al pad is approximately 0.5 ms at 300° C.

[0089] These optimizations are categorized in three main groupscomprising of selecting material properties, the operating parameters,and surface properties. Therefore, minimization of the motion-inhibitingside effect required for proper sonic bearing operations is optimizedwhen the material properties, the operating parameters and the surfaceproperties associated with the sonic bearing operation are individuallyoptimized to inhibit bonding.

[0090] Examples of material property optimizations are (1) selectingmaterials of different crystalline structure for each sliding surface;(2) selecting the material of the sliding surfaces to have high meltingtemperatures; and (3) selecting at least one of the surfaces to have alarge thermal conductivity value. As previously stated, the localultrasonically induced equivalent temperature due to bond breaking atthe asperities site is approximately 1000° C. Therefore, sliding surfacematerials of alumina and tungsten carbide with crystalline structures ofrhombohedral and hexagonal respectively, having melting points of 2015°C. and 2800° C. respectively, in conjunction with tungsten carbidehaving a large thermal conductivity value, will satisfy the aboverequirements.

[0091] Optimizations of the operating parameters include selecting thelowest possible (1) contact pressure, (2) resonant frequency and (3)average operating temperatures for the sliding surfaces. Typically, thebonding pressure for Au on Al in ultrasonic bonding is one hundred timesgreater than the contact pressure of 0 to 1 MPa acting on the slidingsurfaces of a sonic bearing. Generally, the operating frequency forultrasonic bonding is higher than the typical operating frequency of asonic bearing. Lastly, the ambient operating temperature for ultrasonicbonding is around five to ten times higher than the operatingtemperature of 50° C. or lower for a sonic bearing. Therefore, tominimize bonding, it is preferable that each sliding surfaces becontrolled at a temperature between 0° C. and 50° C. It is alsopreferable that the contact pressure between the sliding surfaces beless than 1 MPa. Furthermore, it is preferable to select the frequencyof motion in the bearing element to be a longitudinal acoustic resonantfrequency. Lastly, it is preferred that the frequency of motion in thebearing element be in a range between 0 kHz and 120 kHz to minimizebonding between the sliding surfaces.

[0092] Finally, the sliding surface properties should be optimized by(1) polishing the sliding surfaces to a certain predetermined degree offlatness per unit area to ensure maximum straightness of travel, (2)texturing the sliding surfaces with microscopic recesses in accordancewith a controlled and reproducible pattern to reduce stiction, and (3)coating all the sliding surfaces with a thin film of mineral oilsaturated molybdenum disulfide to perform the dual functions of alubricant and an antibonding agent.

[0093] Another important property of a bearing, besides low friction, isthe bearing's stick-slip characteristic. This type of phenomenon can becommonly found in the squeaking of a door hinge or in the chatter of theaforementioned windshield wiper and is characterized by a semi-irregularoscillatory motion superimposed onto an otherwise smooth, sliding orrotational motion. This semi-irregular oscillatory motion is the resultof fluctuations in the frictional forces along the sliding path. Anecessary requirement for a sliding system to exhibit this stick-sliposcillatory behavior is to have a positive feedback mechanism drivingthe stick-slip relaxation-oscillation mechanism. For two slidingsurfaces, this feedback mechanism can be, for example, the dependance ofthe sliding friction on its sliding speed. Specifically, positivefeedback will occur when the sliding friction decreases with increasingsliding speeds.

[0094] For a bearing, the stick-slip property usually determines theability of that bearing to perform precise, microscopic movements. Inthe case of the sonic bearings of the invention, the bearing's effectivecoefficient of friction μ_(SB) , for a fixed value of the r.m.s.velocity ν_(SB) ^(rms), increases as the speed of the load slidingmotion increases, resulting in a negative feedback rather than apositive feedback to the stick-slip relaxation-oscillation mechanism.The “sonic bearing effect” therefore, not only lowers the bearing'seffective coefficient of friction, but also inherently dampens andprevents the generation of the stick-slip oscillatory behavior. Thestick-slip phenomenon is also well known in the art and are described indetail in the literature. See for example, Blau, P. J., “FrictionScience and Technology”, Mercel Dekker, New York, 1995, pp. 108-134.

[0095] The sonic bearings of the invention can be separated into twodifferent groups depending on whether or not a base member is included.These groups form the two classes of stiff and ultrastiff sonicbearings, with the class having the base member being the ultrastiffsonic bearings. Within both of these classes, the sonic bearings can befurther categorized by the composition of the sonic bearing element.Sonic bearings having a bearing element containing both an activetransducer and an extension member are referred to as indirect-drivesonic bearings and those without an extension member are referred to asdirect-drive sonic bearings.

[0096] The core of any sonic bearing based device is the bearing elementwhich is used to produce the basic oscillatory sliding motions thatdeform and shear the contact asperities at the interface causing theapparent reduction of the effective coefficient of friction and frictionswitching properties. Typically, this element consists of severalsubcomponents including a transducer used to convert an electricalenergy into microscopic mechanical displacements, extension members usedto propagate and possibly amplify the amplitude of the acoustic wavesfrom the transducer source to the sliding surface locations, and contactpad members which provide the actual sliding surfaces.

[0097]FIG. 2A shows a typical transducer 204, which in this case,consists of a bar-shaped piezoelectric transducer with its resonancemodes determined partly by the externally imposed boundary conditions. Aset of coordinate axes are provided whose origin can be used as astationary reference. FIG. 2A also shows one of the simplest mountingtechniques and through it, the imposed acoustic boundary conditions onthe oscillating structure. These boundary conditions can be generallygrouped into the fixed-fixed, fixed-free and the free-free categories.FIG. 2A illustrates the free-free configuration where the transducer 204is held rigidly to the base member 92-1 by a cylindrical support member66-1 located at the nodal region (see FIG. 2B) of the transducer 204.This support member can be made from any solid material or in somecases, may comprise of an element having piezoelectric ormagnetostrictive properties. The support member can also be made frominsulation materials, such as −. However, it should be noted that otherequivalent materials or materials with equivalent properties may be usedas substitutes. The two end surfaces of the transducer, parallel to theXZ-plane, are free to move in a repetitive motion, hence the free-freeboundary condition designation. FIG. 2A further illustrates both thesymmetrical expanding 204E and the contracting 204C phases of thevibrating element. For clarity of illustration purposes, the magnitudeof these microscopic expansions and contractions have been greatlyexaggerated. Typically, the maximum amount of length or Y-axialdisplacement in both the extended and contracted states is less than 0.1percent of its original non-oscillatory length. Again for clarity, theeven smaller displacements associated with the width (X-axialdisplacements) and thickness (Z-axial displacements) dimensional changesof the transducer due to the Poisson effect are also not shown.

[0098]FIG. 2B shows the oscillatory sliding velocities ν_(SB) associatedwith the points on the surface of the piezoelectric transducer havingoscillatory sliding motions that are parallel to the length or theY-axis, as a function of the position along the length. The velocitiesare generated by applying an oscillatory voltage to the transducer.Specifically the electric field, E resulting from the applied voltage tothe upper 68U and lower 68L transducer electrodes interact with thesandwiched piezoelectric material's 69P permanent electric dipolemoment, P to generate the symmetrical microscopic expansions andcontractions of the piezoelectric material. The velocity profile labeledas “+CYCLE” corresponds to the expansion phase 204E of the oscillationcycle of the transducer 204 (see FIG. 2A). Similarly, the “−CYCLE” curveis the velocity profile associated with the contraction phase 204C (seeFIG. 2A) of the oscillation. The “nodal region” on the transducer islocated in close proximity to where the velocity ν_(SB) ^(rms) due toresonant oscillation, is at zero value and conversely, the “anti-nodalregions” are locations near where the oscillatory sliding velocities areat their maximum values (i.e., both +MAX and −MAX value.)

Direct-Drive Stiff Bearing Assembly

[0099]FIG. 3A shows one of the simplest possible sonic bearing designswhich incorporates the previously mentioned transducer. This sonicbearing assembly has only two major components; a bottom, nontranslating section consisting of an active bearing element producingonly oscillatory sliding motions and a moveable, passive, load memberused to support an external load.

[0100] In order to optimize the sonic bearing effect which reduces theeffective coefficient of friction between the bearing element and theload member, it is necessary to select the locations on the bearingsliding surface that are in direct contact with the load sliding surface184-0 of the load member 84-0. In this example, this optimizationprocess is accomplished by attaching additional low mass, very thinplate-shaped upper contact pad members 70U to designated sections of thebearing element where the sliding velocities are at or near theirmaximum values. Using the theoretical information from FIG. 2B, thesemaximum velocity locations or regions on the bar-shaped bearing elementare the anti-nodal regions. The resulting modified geometry of thebearing element will now contact the planar load sliding surface 184-0of the load member 84-0 only at the element's anti-nodal regions.

[0101] The bearing element in FIG. 3A consists of a bar-shapedpiezoelectric transducer with four upper plate-shaped contact padmembers 70U affixed, using an adhesive means, to the anti-nodal regionsof the upper electrode surface 168U. The upper 68U and lower 68Ltransducer electrodes are electrically connected to an excitation driver(not shown) through two conventionally attached upper 74U and lower 74Lexcitation wires and produce an electric field, E. The interaction ofthe electric field, E with the electric dipole moment, P of thepiezoelectric material generates microscopic oscillatory sliding motionhaving a specific root-mean-square velocity. The bearing element canresonate in its length dimension (parallel to the Y-axis) at its lowestlongitudinal acoustic resonant frequency and can be supported at thenodal region of the lower transducer electrode 68L by a support memberwhich in turn, can be rigidly secured to an external platform. However,an electronic signal of a predetermined frequency and magnitude maybeapplied to the bearing element to cause the bearing element to oscillateat a different root-mean-square velocity.

[0102] The sonic bearing assembly also consists of a load member 84-0having a planar load sliding surface 184-0 which is in direct slidablecontact, defined as an interface, with the four symmetrically placedcontact pad surfaces 170U. The bearing sliding surface, in thisembodiment, comprises of the four contact pad surfaces 170U and theexposed upper electrode surface 168U. Although the bearing slidingsurface comprise the surfaces of the four contact pad members 70U, itmust be appreciated that the contact pad members 70U are not necessaryto practice the invention. The load member 840, which supports anexternal load on the load accepting surface 284-0, can slide in any pathdirection 48-2 within the plane defined by the four contact pad surfaces170U with an apparently reduced coefficient of friction or effectivecoefficient of friction. However, it must be noted that although theload accepting surface 284-0 is opposite to the load sliding surface184-0 in this embodiment, the load accepting surface 284-0 does notnecessarily have to be configured as such.

[0103] An equally viable and useful alternate sonic bearing design isthe inverse of the sonic bearing described in FIG. 3A. For this inverseembodiment (not depicted), the sonic bearing configuration also has twomajor components, consisting of an upper movable component whichcontains the active bearing element that can slide on a lower passive,stationary, load member. However, unlike the design shown in FIG. 3A,where an external load can be placed on any part of the load acceptingsurface 284-0, the bearing element of this inverse configuration (notshown) supports an external load placed only at the bearing element'snodal region. In practical applications where only friction reduction,friction switching, and precision guidance are required, the designillustrated in FIG. 3A, its inverse and their equivalents aresufficient. However, because the stiffness characteristic of a bearingis of paramount importance in many other bearing applications, therudimentary designs illustrated by these examples must be modified toincrease stiffness in the bearing element to suit those otherapplications.

[0104] This lack of stiffness in these rudimentary sonic bearing designscan be directly traced to the method in which the bearing element andthe external load are supported. For example, in the case where theexternal load is supported by the bearing element only at the nodalregion and the bearing element itself is supported by the stationaryload member at the anti-nodal regions, the cantilever-like structureformed by the distance between the nodal region and any anti-nodalsupport region is the root cause of the stiffness problem.

Indirect-Drive Stiff Bearing Assembly

[0105] One solution to this stiffness problem is the indirect-driveconfiguration. Indirect-drives are composite bearing element structureswhere at least one active transducer and one or more extension membersresonate at the same frequency and are mechanically coupled togethernear their individual respective minimum acoustic impedance locations.The physics of the selected acoustic mode and the coupling mechanism ofthese indirect-drive elements rely on the principle of sympatheticresonance which dictates the transfer of acoustic energy between anactive transducer and each passive resonating extension member attachedthereto.

[0106] One simple mechanical design of an indirect-drive sonic bearingis shown in FIG. 3B which is similar to the optical photoelasticmodulator device described in U.S. Pat. No 3,867,014 issued to Kemp(1975). As shown, the transducer element, with upper and lowerelectrodes 68U and 68L having two conventionally connected excitationwires 74U and 74L respectively, is attached to an extension member 78-0and both resonate at the same lowest longitudinal frequency. The load issupported by the load member 84-1 on the load accepting surface 284-1and the load sliding surface 184-1 of the load member is in slidablecontact with the upper contact pad surfaces 170U of the contact padmembers 70U on the extension member 78-0 allowing load sliding motionalong the path direction 48-2.

[0107] The advantage of this configuration is to be able to freelyselect a material for an extension member without consideration of itspiezoelectric properties and use it as a stronger support for the entirebearing element and an external load. For example, because the stiffnessof a cantilever is directly proportional to its Young's modulus, if atungsten carbide material is used as the extension member, the stiffnessof the cantilever-like structure of the bearing element can be increasedby nearly ten times over the most common transducer material, leadzirconate titanate.

[0108] Indirect-drive bearings can be even further stiffened byattaching the nodal regions of each transducer and each extension memberto the same external platform. By doing this, the cantilever-likestructure is transformed into an arch-like structure which increases thebearing element stiffness by an additional factor of approximatelysixteen.

Ultrastiff Bearing Assembly

[0109] A better and more straightforward solution to this stiffnessproblem is to modify the bearing element so that there are contact padmembers on both the upper and lower surfaces. In this new ultrastiffbearing element configuration, the load can now be supported directly bythe material in the cross section containing the contact pad membersinstead of through the cantilever between the nodal and anti-nodalregions. The stiffness of the sonic bearing assembly, with thismodification, is then changed from the relatively low stiffness of acantilever system to the very high compressive stiffness of the bearingelement's materials.

[0110] To illustrate the improvement that this solution offers, we cancalculate the theoretical intrinsic compressive stiffness of thisbearing element configuration from the material stiffness equationderived from the basic equation for the modulus of elasticity

[P_(APP)]_(Z)=(Y_(BE))(ΔZ_(BE))/(Z₀),

[0111] where [P_(APP)]_(Z) is the Z-axis component of the appliedpressure on the material of the load bearing portion of the bearingelement, Y_(BE) is the modulus of elasticity or Young's modulus of thatmaterial, Z₀. is the thickness of that material, and ΔZ_(BE) is thechange in the thickness of that material which is produced by thepressure [P_(APP)]_(Z) Substituting the expression of the Z-axiscomponent value of the force [F_(APP)]_(Z) divided by the materialsurface area A_(BE) for [P_(APP)]_(Z) and rearranging the equation, wearrive at an expression equivalent to the well known spring-forceequation

[F_(APP)]_(Z)=(k_(BE))(ΔZ_(BE)) ,

[0112] where k_(BE) is the equivalent spring stiffness or rather, forthis discussion, bearing element stiffness given by the followingequation

k_(BE)=(A_(BE))(Y_(BE))/(Z₀) .

[0113] For a sonic bearing element operating at its lowest longitudinalacoustic resonant frequency mode with, for example, an operatingfrequency of motion of around 35 kHz, the area A_(BE), which is thetotal area of the contact pad surfaces, is about 1×10⁻⁴ m². The bearingelement thickness Z₀ is typically around 3×10⁻³ m and if an alloyedmaterial of tungsten carbide and cobalt is used as the load bearingportion of the bearing element, Young's modulus Y_(BE) can be as high as6×10¹¹ N/m². Substituting these values into the bearing elementstiffness equation above yields a theoretical intrinsic stiffness ofabout 2×10¹⁰ N/m ( 114 lbs/μin ).

[0114] This intrinsic, non-servoed compressive stiffness of the sonicbearing is already substantially larger than the stiffness of, forexample, a servoed system such as a typical air bearing, which has atypical stiffness value of several million pound-force per inch orapproximately 1×10⁹ N/m. Furthermore, as it will be shown later, thestiffness of a sonic bearing assembly employing a “force servomechanism” can easily be one thousand times larger than its ownintrinsic value and by comparing these two servoed systems, it willbecome evident that a sonic bearing is substantially stiffer than an airbearing whereby use of the term “ultrastiff” for describing sonicbearings is clearly justifiable.

[0115] A typical embodiment of an ultrastiff sonic bearing assembly is athree-layered sandwich, plain bearing-like structure comprising amoveable load member with a load accepting surface and load slidingsurfaces, a resonance-enhanced, longitudinal acoustic wave drivenbearing element with upper and lower contact pad surfaces, and astationary base member with a base sliding region. The load slidingsurface is in continuous slidable contact, along an upper interface,with the upper contact pad surfaces of the bearing element andsimilarly, the lower contact pad surfaces of the bearing element are incontinuous sliding contact, along a lower interface, with the basecontact pad surfaces within the base sliding region. In this embodiment,the individual geometries of the load, base structures and the bearingelement can all be bar-shaped parallelepiped with their sliding surfacesmicroscopically textured and polished optically flat. Also, aspreviously mentioned, the bearing stiffness and durability can beenhanced by choosing the materials for the load bearing portion of thebearing element from very hard and stiff substances such as diamond,tungsten carbide, alumina or stainless steel.

[0116] Furthermore, a multitude of these bearings can be used toconstruct a composite bearing structure, such as a linear stage wherethe individual bar-shaped structures for each bearing may be integratedinto the stage's internal structures and may therefore lose theiroriginal parallelepiped geometry.

Direct-Drive

[0117] Ultrastiff direct-drive bearing assemblies contain some of thesimplest possible ultrastiff bearing element configurations and anexample of one such configuration is shown in FIG. 4A. This sonicbearing element consists of a bar-shaped parallelepiped piezoelectrictransducer with eight attached plate-shaped parallelepiped contact padmembers. Each contact pad member has a contact pad surface and anoppositely facing pad attachment surface, and both of these surfaces areparallel to the XY-plane. Both the transducer and the contact padmembers have their longest dimension being defined as their length andare parallel to the Y-axis. The next largest dimension is their widthwhich is parallel to the X-axis and the smallest dimensions is theirthickness which is parallel to the Z-axis. In the case shown in FIG. 4A,the transducer is the bare piezoelectric transducer and the bearingelement body is the mechanical body of the piezoelectric transduceritself. The bearing sliding surface of the bearing element 100 consistsof the exposed portion of the upper electrode surface 168U and thecontact pad surfaces 170U of the four upper contact pads 70U. Thebearing support region of the bearing element 100 consists of theexposed portion of the lower electrode surface 168L and the contact padsurfaces 170L of the four lower contact pads 70L.

[0118] The electric dipole moment direction, P of the piezoelectricmaterial 69P is perpendicular to the upper 168U and lower 168L electrodesurfaces. The upper 68U and lower 68L transducer electrodes areelectrically connected to an excitation means (not shown) through twoconventionally attached upper 74U and lower 74L excitation wires.

[0119] The four pad attachment surfaces of the upper contact pad members70U are glued to the transducer electrode surface 168U such that theircontact pad surfaces opposite the pad attachment surfaces are theinterface of the bearing sliding surface. Similarly, the contact padsurfaces of the four lower contact pad members 70L collectively form theinterface of the bearing support region.

[0120] The bearing element 100 with a symmetrically positionedcylindrical support member 66-1 is operated at its lowest longitudinalacoustic resonant frequency mode (i.e., fundamental frequency or λ/2mode) where the length-to-width ratio is selected to simultaneouslyobtain high electromechanical coupling coefficient κ₃₁ and awell-isolated longitudinal acoustic resonant frequency. The lowestresonant frequency is determined mainly by the longest dimension of thebearing element, which in this case, is its length. The axis parallel tothe bearing element dimension, which mainly determines the selectedresonance frequency, is also known as the resonant axis. For the lengthmode longitudinal resonance bearing element shown in FIG. 4A, theresonant axis is the Y-axis.

[0121] All the contact pad members are placed where in theroot-mean-square velocity of the bearing element parallel to the Y-axisis within a predetermined range or percentage of the maximum of theroot-mean-square velocity. In other words, the contact pad members areplaced at locations where the oscillatory sliding motions of thetransducer are at or near their maximum amplitudes and simultaneouslythe mechanical oscillations perpendicular to the Y-axis, due to thePoisson effect, are near their minimum values. The use of very low masspads, along with symmetrical placements of these pads on the bearingelement, ensures that the resulting direct-drive bearing element'soscillation mode is essentially identical to the original unmodifiedtransducer mode. A general description of the resonant modes ofpiezoelectric transducer is given by R. Holland et al., “Design ofResonant Piezoelectric Devices”, Research Monograph No 56, M.I.T. Press,Cambridge, Mass., 1969.

[0122] Another type of electromechanical transducer that can be used inthe direct-drive bearing element configuration may be of the typecomprising a laminated core of magnetostrictive material, such asTerfenol available from Etrema Products Inc., Ames, Iowa, for example,as shown in FIG. 4B. In this example, an excitation coil 68E is woundaround the magnetostrictive material 69M and is electrically connectedto an alternating current source and a direct current source (both notshown) by the excitation wires 74U and 74L such that he resultingmagnetic field B established by the excitation coil causes themagnetostrictive material to elongate and contract in accordancetherewith. Like the design of FIG. 4A, the bearing element 101 of FIG.4B has four upper contact pad surfaces 170U of the upper contact padmembers 70U glued to the upper transducer surface to form the interfaceof the bearing sliding surface. Similarly, the lower contact padsurfaces 170L of the four lower contact pad members 70L collectivelyform the interface of the bearing support region. Also, the bearingelement 101 has a symmetrically positioned cylindrical support member66-1 and is operated at its lowest longitudinal acoustic resonantfrequency mode (i.e., fundamental frequency or λ/2 mode) along thelength dimension of the bearing element.

[0123] A bearing element with vertically (i.e., along the Z axis) orhorizontally (i.e., along the X or the Y axis) stacked transducers insuccession can also be used to construct a direct-drive ultrastiffbearing element and examples are shown in FIGS. 4C and 4D. FIG. 4Cillustrates an ultrastiff direct drive sonic bearing element 102 withseveral piezoelectric transducers vertically stacked in succession. Thebearing element is also shown to have an upper surface 168U with fourcontact pad members 70U attached to the corners of the XY-plane bearingfaces resulting in the establishment of the four upper contact padsurfaces 170U. The bearing element 102 has an upper excitation wire 74Uconnected to the upper transducer electrode 68U and a lower excitationwire 74L connected to the lower transducer electrodes 68L.

[0124] In FIG. 4D, the horizontally (i.e., along the Y axis) stackeddevice consists of several piezoelectric transducers in succession withalternating dipole moment directions, P sandwiched by front 68F and back68B transducer electrodes. All the front electrodes 68F are connected toa front excitation wire 74U and similarly, all the back electrodes 68Bare conventionally attached to the back excitation wire 74L. Thecollective edge surfaces of the transducer materials and electrodes thatare parallel to the XY-plane are upper and lower bearing faces. The fourupper 70U and four lower 70L contact pad members are attached to thecomers of the XY-plane bearing faces. The four upper contact padsurfaces 170U along with the exposed section of the upper bearing faceis the bearing sliding surface and similarly, the exposed portion of thelower bearing face in conjunction with the lower contact pad surfaces170L forms the bearing support region.

[0125] Like the design in FIG. 4A, the centrally positioned cylindricalsupport member 66-1 (shown in FIGS. 4C and 4D) is used to rigidly attachthe longitudinal fundamental mode, stacked, direct-drive, ultrastiffbearing element to other components. The main purpose of thissegmentation of the piezoelectric material is to reduce the magnitude ofthe applied A.C. oscillatory and/or D.C. excitation voltages necessaryto obtain a predetermined level of transducer activity. This techniqueof stacked piezoelectric design as described in U.S. Pat. No. 1,860,529of Cady (1932) and is old in the art.

[0126] The various standard definitions of the piezoelectric transducerrelated terms such as K₃₁ and poling direction can be found in “Guide toModem Piezoelectric Ceramics”, published by Morgan Matroc, Inc.,Bedford, Ohio or “Piezoelectric Ceramics”, printed by ChannelIndustries, Inc., Santa Barbara, Calif., “Piezoelectric Ceramics”,published by EDO Corp., Salt Lake City, Utah or “MultilayerPiezoelectric Actuators: User's Manual”, Vol. 2, printed by TokinAmerica Inc., San Jose Calif.

Indirect-Drive

[0127] Ultrastiff indirect-drive bearing assemblies contain bearingelements that are composite structures which also use the principle ofsympathetic resonance to couple the acoustic energy between an activetransducer and a resonating extension member. Examples of these types ofelements are those illustrated in FIGS. 5A through 5E. The mechanicaldesign of the ultrastiff indirect-drive bearing element in FIG. 5A iscomparable to that of FIG. 3B with additional lower anti-nodal contactpad surfaces in the bearing support region. The design of FIG. 5B issimilar to that of FIG. 5A but illustrates the use of a magnetostrictivetransducer instead of a piezoelectric transducer. A dual transducer,ultrastiff indirect-drive sonic bearing element is illustrated in FIG.5C, which shares many similarities with the mechanical structure of anAcoustic Transformer Powered Super-High Isolation Amplifier devicedescribed in National Semiconductor Application Note 285. The quadtransducer, ultrastiff indirect-drive sonic bearing element illustratedin FIG. 5D can be seen as a simple extension of FIG. 5C. And, lastly,the indirect-drive stepped horn design shown in FIG. 5E is analogous tothe wire bonder configuration as revealed in U.S. Pat. No. 5,244,140 ofRamsey et al., (1993). However, for the embodiment of FIG. 5E, two hornsare driven simultaneously by a single transducer element.

[0128] The three main advantages of ultrastiff indirect-drive bearingelement designs are (1) the separation of the electromechanicaltransducer processes from the purely mechanical bearing requirements,(2) the extension of the bearing element's length without lowering thebearing element's ultrasonic operating frequency into the audio range,and (3) the mechanical amplification of the transducer displacementswhich produce the oscillatory sliding motion of the bearing slidingsurfaces.

[0129] The dimensions of an extension member body are variable and thusmay be altered, such as along one or more dimensions to maximize energycoupling efficiency to the transducer, or in some cases, along its crosssection, to dynamically configure the extension member to changes inforce applied to the bearing assembly. Furthermore, it is desirable tominimize any motion-producing and motion-inhibiting phenomena betweenthe load member and the extension member body. This is done bydetermining a common resonant frequency, an individual resonant phase,and an individual resonant amplitude for the motion of the contactpoints on the extension member. Then, the frequency of the motion is setto produce a resonance along the propagation direction in the extensionmember; whereby the propagation direction of the resonant wave isaligned substantially parallel to the extension sliding surface.Following, the phase and amplitude of the contact points in theextension member are set to the resonant phase and amplitude.

[0130]FIG. 5A shows one of the simplest ultrastiff indirect-drivebearing element configurations. A transducer consisting of a bar-shapedpiezoelectric transducer with upper 68U and lower 68L transducerelectrodes, upper 168U and lower 168L (not shown) electrode surfacesconnected to corresponding upper 74U and lower 74L excitation wires. Thepiezoelectric transducer's electric dipole moment direction, P isparallel to the Z-axis. The transducer is joined end-to-end, in theZX-plane, to a single bar-shaped λ/2 extension member 78-1 along theextension attachment face using a glue as the adhesive means. Theextension member 78-1 has an extension member body 578-1, and twoextension member faces of the extension member 78-1 which are parallelto the XY-plane. The extension member 78-1 is equipped with plate-shapedupper 70U and lower 70L contact pad members having corresponding upper170U and lower 170L contact pad surfaces. As in the case of the directdrive sonic bearing configuration, the four upper contact pad surfaces170U along with the exposed section of the upper extension member facecollectively becomes the bearing sliding surface. Likewise, the lowercontact pad surfaces 170L plus the uncovered portion of the lowerextension member face make up the bearing support region. Both thetransducer and the extension member are resonating in the λ/2longitudinal acoustic mode with the cylindrical support members 66-1,66-2 connected to their respective nodal regions. The transducer, theextension member and the associated contact pad members collectivelyform the ultrastiff indirect-drive bearing element. As stated earlier,another type of electromechanical transducer that can be used may be ofthe type comprising a core of magnetostrictive material. Anindirect-drive bearing element configuration using this type oftransducer is shown in FIG. 5B which operates in a fashion similar tothat of FIG. 4B. In FIG. 5B, however, an excitation coil 68E and apolarization coil 68P are wound through a rectangular slot in a coremade of magnetostrictive material 69M. The excitation coil iselectrically connected to an alternating current source (not shown) bythe excitation wires 74U and 74L and the polarization coil iselectrically connected to a direct current source (not shown). Theresulting magnetic field, B established by the excitation coil and thepolarization coil causes the core to elongate and contract in accordancetherewith so as to produce a resonance. Also, in this design like thatof FIG. 5A, there is an axially attached extension member 78-1 whichalso resonates at the same frequency.

[0131] FIG. SC illustrates a variation of the indirect-drive bearingelement design where two identical bar-shaped piezoelectric transducersare used to drive a single bar-shaped λ/2 extension member 78-2 equippedwith upper 70U and lower 70L contact pad members on the upper and lowerextension member faces respectively. All three elements are oscillatingat the same frequency and in the same λ/2 longitudinal acoustic lengthresonant mode. The cylindrical support members 66-1,66-2 are used toattach this dual indirect-drive bearing element to other componentswithout damping the oscillatory sliding motion. The two upper 168Uelectrode surfaces, the upper λ/2 extension member's face parallel tothe XY-plane and the four upper contact pad surfaces 170U collectively,form the bearing sliding surface. The bearing support region consists ofthe lower four contact pad surfaces 170L together with the exposedsection of the lower extension member face. The main advantage of thisconfiguration is that the sonic bearing can support a much heavier load.

[0132] An extension of the bearing element of FIG. 5C is anindirect-drive bearing element using a quad transducer drive. FIG. 5Dshows such an indirect-drive design, consisting of four,length-resonant, λ/2 mode piezoelectric transducers, each having fourupper 70U and four lower 70L contact pad members attached to the upper168U and lower 168L electrode surfaces respectively, driving a frequencymatched square extension member 78-4. In this configuration, thecross-shaped bearing element structure can be rigidly attached via thefive cylindrical support members 66-1, 66-3 to a base member and cansupport a substantial load.

[0133] The resonant frequencies of any transducers and any coupledextension members should be matched to within 0.1 percent. When thetransducer and the extension member frequencies are properly matched,the adhesive means used to join the two end surfaces together can be avery low tensile strength glue, such as a RTV silicone elastomer. Themain advantage of the precision frequency matching and the use of verylow tensile strength adhesive to join the active and passive elements isto prevent excitation of parasitic transverse oscillatory modes in thecoupled system.

[0134] The acoustic coupling efficiency can also be optimized bymatching the acoustic impedances of the transducer and the extensionmember as similarly described in the acoustic microscope method used by“C. F. Quate et al., “Acoustic Microscopy with Mechanical Scanning-AReview”, Proc. IEEE, Vol 67, 1979, pp. 1092-1114. For example, if thecoupling surface areas for both the transducer and the tungsten carbideextension member are identical as in FIG. 5A, the calculatedlongitudinal acoustic energy coupling efficiency between the transducerand the tungsten carbide extension member is approximately 70 percent.However, if the tungsten carbide extension member's surface area isreduced as shown in FIG. SC, the acoustic coupling efficiency can nowapproach 100 percent.

[0135] The proper operation of the extension member in the longitudinalacoustic resonant mode or any other resonant mode can be directly viewedand verified by using a Fizeau interferometer with a 150 mm beamdiameter available from Phase Shift Technology, Tucson Ariz. Theinterferometer is used to directly view the submicron-size thicknessmodulations in the transducer and the extension member's nodal locationsdue to the Poisson effect.

[0136] The bearing element design shown in FIG. SE is a singlebar-shaped piezoelectric transducer with upper 68U and lower 68Ltransducer electrodes and corresponding upper 74U and lower 74Lexcitation wires driving two extension members which are stepped horns82 each located at one of the transducer's end faces. The electricdipole moment direction, P of the transducer material is perpendicularto the upper 168U and lower 168L electrode surfaces (i.e., parallel tothe Z-axis). Both the transducer and the horns are tuned to the samelongitudinal acoustic resonant frequency. In particular, in this case,all three elements are operated in their longitudinal fundamental lengthresonant modes (i.e.,λ/2) with each horn's step located at theirrespective horn's mid-length or λ/4 position. The upper and lower faceson the horn are parallel to the XY-plane. Four upper 70U and four lower70L, low mass, plate-shaped, contact pad members are placed near theoutput or back end of the two horns' faces to provide the four upper170U and four lower 170L contact pad surfaces. The complete bearingassembly has a mechanical attachment via the cylindrical support member66-1 position and is affixed to the transducer's nodal region.

[0137] The purpose of using a horn rather than a much simpler bar-shapedextension member is the ability of a passive horn body, 582 tomechanically amplify the microscopic ultrasonic oscillatorydisplacements produced by the transducer. Generally, all acoustic hornsand in this case, stepped horns have a front end or input face with alarger input face area 182F, and a back end or output face having asmaller output face area 182B. Any XZ planar longitudinal ultrasonicwaves with displacements along to the Y-axis at the input face can beamplified by the horn at the output face. Since the oscillationfrequencies of both ends of the horn are identical, the r.m.s. velocityof the ultrasonic wave displacements at the output end is alsocorrespondingly amplified. The amplification gain factor and theresonant frequency for a horn of a given length depend upon the detailedgeometry of the taper (e.g., stepped, linear, conical, exponential orcantenoidal), the ratio of input/output cross sectional areas and othermiscellaneous parameters, such as the velocity of sound in the hornmaterial.

[0138]FIG. 6A shows an exploded view of one of the simplest andtherefore the lowest cost ultrastiff sonic bearing designs. The bearingelement 100 (see FIG. 4A for the detailed definitions of the bearingelement 100 such as the upper and lower contact pad members, the upperand lower transducer electrodes, and the upper and lower electrodesurfaces) is a direct-drive structure operating in the λ/2 longitudinalresonant mode. The transducer element is selected for its high qualityfactor Q, and for the specific case of lead zirconate titanate types oftransducers, such as PZT8 from Morgan Matroc, Ltic., Bedford Ohio, themaximum Q is around 1000. The bearing element of this sonic bearingdesign has dimensions of 46 mm long by 25 mm wide and 3 mm thick andwill resonate in the longitudinal λ/2 mode at approximately 35 kHz. Theeight microscopically textured and optically flat (to one-quarterwavelength of a red HeNe laser) tungsten carbide contact pad members,with dimensions of 5 mm by 5 mm by 0.5 mm thick, are secured by anadhesive means at the four corners of the two transducer electrodesurfaces. The adhesive means is 50 to 100 microns thick layer of glueused to attach the four upper 70U and four lower 70L contact pad membersto the corresponding upper 168U and lower 168L piezoelectrictransducer's nickel electrode surfaces. The glue should have very hightensile strength such as Devcon 10760 Titanium Putty from ITW Devcon,Danvers Mass.

[0139] The load member 84-2 has a load accepting surface 284-2 and anoppositely facing load sliding surface 186. A portion of the loadsliding surface is the microscopically textured, optically flat (toone-quarter wavelength of a red HeNe laser) 5 mm wide by 5 mm thick by70 mm long ISO M20 grade tungsten carbide surfaces of the load guidewaymembers 86. The base member 92-2 has a base sliding region 192-2 and anoppositely facing base platform region 292-2. Embedded in the basemember are four 5 mm by 5 mm by 2 mm thick tungsten carbide base contactpad members 96. The sections of the base sliding region which are thecontact pad surfaces 196 have been textured and polished optically flatto form a single plane. Both the load guideway members 86 and the basecontact pad members 96 are attached to the load member 84-2 and the basemember 92-2 respectively by an adhesive means such as glue.

[0140] The bearing element 100 is both aligned and fixedly mounted tothe base member. The technique consists of securing the nodal region(not shown, but see FIG. 2B) on the lower transducer electrode surface168L to a 6 mm diameter by 6 mm long cylindrical support member 66-1made of an insulator material, such as Al₂O₃, using an adhesive means.The cylindrical support member 66-1 in turn, is aligned and glued to thelower base member 92-2 on the Z-axis compliant base support memberregion 67 such that the four lower contact pad surfaces 170L (not shown,but see FIG. 4A) are parallel to and in sliding contact with the fourbase contact pad surfaces 196 of the base sliding region. Similarly, thefour upper contact pad surfaces 170U of the bearing sliding surface areparallel to and in slidable contact with the load guideway surfaces 186of the load sliding surface. The directions of the sliding movements ofthis sonic bearing's load member 84-2 relative to the fixed base memberare shown by the translational direction arrows 48-1.

[0141] The embodiment of FIG. 6B is similar to that of FIG. 6A exceptthat all eight lower sliding surfaces comprising of the four lowerbearing contact pad surfaces 170L (not shown, but see FIG. 4A) of thebearing support region and the four base contact pad surfaces 196 of thebase sliding region are modified by the lower lubrication means.Specifically, this lower lubrication means consists of a molybdenumdisulfide and mineral oil mixture which is held in a lower reservoirstructure formed by the combined surfaces of the bearing support region,the base sliding region and the lower RTV silicone elastic seal 90. Aspacer 98 attached by four screws 88 to the base member 92-2 is part ofan upper oil reservoir structure which is used to lubricate the sixupper sliding surfaces comprising of the four upper contact pad surfaces170U of the bearing sliding surface and the two load guideway surfaces186 of the load sliding surface. The surfaces which enclose the upperoil reservoir are the load sliding surface, the bearing sliding surfaceand a portion of the upper elastic seal 90 surface. This upper reservoirwith its molybdenum disulfide and mineral oil mixture is the upperlubrication means for the sonic bearing.

[0142] It should be noted that the load sliding surface, the bearingsliding surface, bearing support region and base sliding region have asurface material which may be comprised of: diamond, diamond-like carbonmaterials, steel alloys, steel, cubic carbon nitrides, cubic boronnitrides, zirconium carbon nitrides, titanium carbon nitrides, titaniumaluminum nitrides, aluminum alloys, aluminum, alumina, sapphire, W, Ni,Nb, Ti, Si, Zr, Cr, Hf, Y, oxides of Nb, oxides of Ti, oxides of Si,oxides of Zr, oxides of Cr, oxides of Hf, oxides of Y, carbides of W,carbides of Nb, carbides of Ti, carbides of Si, carbides of Zr, carbidesof Cr, carbides of Ta, carbides of Hf, nitrides of Ti, nitrides of Si,nitrides of B, nitrides of Zr, borides of W, borides of Zr, borides ofTi, borides of Hf, borides of Cr, PTFE polymer, HDPE polymer, and UHMWPEpolymer.

[0143]FIG. 7A shows a block diagram of the drive electronics package 500which can be used to oscillate any bearing elements equipped with atleast one piezoelectric transducer 204. The basic drive electronicspackage contains an excitation means 200, which is designed to oscillatethe piezoelectric transducer at any one of the transducer's minimumimpedance frequencies. The basic package can be expanded to furtherinclude, in any quantity and combination, an oscillation levelcontrolling means 202 which will allow for the control of the r.m.s.velocity of the oscillatory sliding motion, a cross section controllingmeans 206 which will allow for adjustments of the cross section alongthe length of the bearing element independent of the oscillation, and ahigh voltage bias means 330 which will establish an initial electricfield, E in the transducer 204. Each of these components of theelectronic package can be implemented entirely by using conventionalanalog electronic devices or in some combination with digital deviceswhich may include one or more microprocessors.

[0144] The circuit of the excitation means 200 senses the current, iflowing through the transducer 204 at the lower transducer electrode 68Lvia the lower excitation wire 74L and converts that current into anequivalent voltage using a wide band current-to-voltage amplifier 304.The resulting voltage signal is sent through a high Q electronicband-pass filter 306 to select the correct transducer oscillation mode.Finally, the signal is appropriately phase shifted by a constantamplitude phase shifter circuit 314 to obtain the required zero phasepositive feedback oscillatory condition for the selected frequency. Theprocessed voltage signal from the phase shifter is then used as input toan excitation driver 316 which uses a fixed or variable D.C. low voltagesupply to determine the maximum oscillation amplitude. This excitationdriver 316 uses a “half-bridge” drive configuration whose square waveoutput is then available to excite the piezoelectric transducer's upperelectrode 68U via the upper excitation wire 74U which completes theoscillator feedback loop. The unidirectional electric field, E generatedby the driver's low voltage square wave interacts with the piezoelectricmaterial 69P having a fixed electric dipole moment, P to convert aportion of the electrical energy into acoustic vibrations.

[0145] The transducer's oscillation level can be controlled by thecircuit of the controlling means 202 which includes a processing unit310 for dynamically changing the output of the adjustable D.C. lowvoltage supply 318 in order to maintain a constant r.m.s. value fortransducer current, i. This processing unit 310 functions by comparingthe r.m.s. value of the filtered and phase shifted signal representingthe sensed transducer current, i from the phase shifter 314 with anexternally programmed excitation level 312. Any difference between ther.m.s. value and the level value generates an error signal which is thenused to change the amplitude of the low voltage square wave by changingthe output level of the adjustable D.C. low voltage supply 318. There isalso provided an effective coefficient of friction, “μ_(SB) levelcontrol” input to the excitation level 312 for external modulation ofthe sonic bearing's effective coefficient of friction μ_(SB).

[0146] Furthermore, as it will be discussed in detail later, because abearing element can also act as a sensing means to determine themagnitude of the normal component of the force acting on that bearingelement, the processing unit 310 further functions to generate a “forcesensor output” signal, which is proportional to this magnitude of theforce. This “force sensor output” signal can be used in a feedbackmechanism in a multi-bearing element assembly to maintain the fidelityof the load sliding motion with respect to the desired slidable path andto control the force.

[0147] The second controlling means 206 can be employed to alter thecross section of a bearing element along one dimension thereof in acontrolled fashion. For a direct-drive bearing element whose slidingsurfaces are attached to a piezoelectric transducer, this cross sectioncontrol consists of supplying a predetermined high voltage signal to thepiezoelectric transducer itself. In the circuit of the controlling means206, the processing unit 322 compares the value of an external servoinput signal with a programmed reference level 320 such that an errorsignal representing a needed cross sectional change can be generated andthen used to change the output level of the adjustable high voltagesupply 326. This output level can then be summed in the summing unit 324with the low voltage square wave from the excitation driver 316 of theexcitation means 200 and transferred to the transducer accordingly.

[0148] Being able to controllably change the bearing element crosssection, specifically along its length (i.e., being able to change inthickness and/or width dimension), in conjunction with the fact thateach bearing element can act as a force sensing means, allows forservoed control of a sonic bearing assembly's stiffness.

[0149] In a multi-bearing element sonic bearing assembly wherein thebearing elements have an appropriate geometric relationship thisstiffness servo is achieved by maintaining the force acting one of thebearing elements to be constant. One such relationship can be found inthe simple case of two rigidly fixed and opposing bearing elementssandwiching the same load member. For this example, the external servoinput signal for one bearing element is a “force servo input” signalwhich can be taken directly from the “force sensor output” of theprocessing unit 310 of a another bearing element electronics package500. In this way, any change in force away from the bias force referencelevel 320 on one bearing element due to, for example, thermal expansion,wear, or an external force on the load member will be sensed and therebycause the opposing bearing element to restore the force by altering itsappropriate dimension.

[0150] Furthermore, if both feedback mechanisms are employed in theaforementioned relationship (i.e., the “force servo input” for onebearing element is the “force sensor output” of the other and viceversa), the dynamic range of servo adjustment can be substantiallyincreased. In this type of assembly the processing unit 322 in eachelectronics package can additionally use the internally generated “forcesensor output” signal from the processing unit 310 associated with thesame bearing element in order to provide additional control features.

[0151] The reference level 320 of the controlling means 206 is alsoprovided with an external control input which can be used for modulatingthe bearing cross section. More particularly, for the aforesaidmulti-bearing element application, this external control input can be a“force control” signal which when used in conjunction with the “μSBlevel control” signal provides for the possibility of control over bothinput parameters of the frictional sliding force equation (i.e.,F_(FRIC)=μ_(SB)[F_(APP)]_(Z)). This complete control over frictionsliding force translates directly into control over the applied slidingforce needed to slide a load.

[0152] Lastly, an additional high voltage signal from the bias means 330can be summed in the summing unit 324 with the signal from theexcitation driver 316 in order to provide an electrical bias on thetransducer in addition to the square wave output. This bias is usefulfor shifting the operating region of transducer devices with nonlineardisplacement characteristics, such as those using electrostrictivematerial, to a region having higher linearity. This high voltage bias isalso provided with an external control input for externally altering thelevel of the applied voltage bias if desired. This external level setcan be a signal generated from an external sensor, such as thoseemployed in the use of interferometry, strain detection, or capacitivesensing,

[0153] Applying a high voltage to the piezoelectric transducer canproduce changes in the dimensions of the transducer element itself aslarge as 0.02 percent and these changes are governed by the equations ofdisplacement as defined in the literature for a piezoelectric materialand are well known in the art. However, this ability of a sonic bearingelement to simultaneously oscillate vigorously and controllably change,for example, its thickness between the bearing sliding surface and thebearing support region , both actions operating substantiallyindependent of each other, is a primary feature of the invention. Thisunique property is made possible by the fact that: (1) for a high Qbearing element (e.g., Q greater than 1000), the maximum peak-to-peak,oscillation producing, excitation voltage that can be applied across thetransducer before reaching material destruction pressure is only a smallfraction (viz, less than three percent) of the electrical breakdownvoltage and (2) the maximum piezoelectric material expansion when avoltage near the electrical breakdown voltage is applied is only a smallfraction (viz, less than five percent) of the material expansion limit.Therefore, a bearing element excited to near its maximum oscillatorydisplacement condition can still change its thickness₁₃ between thebearing sliding surface and the bearing support region by theapplication of a very large quasi-DC voltage.

[0154]FIGS. 8A to 8F illustrate the effect on the bearing elementthickness by applying an additional high voltage as used in thecontrolling means 206 option and the bias means 330 option and itsindependence from the oscillatory behavior of the bearing element. InFIGS. 8A to 8C a sectional view of thickness modulation along the lengthof the bearing element 100 due only to the induced longitudinal lengthresonant oscillation of the λ/2 mode is shown for individual phases ofthe oscillation. FIG. 8A corresponds to the extreme of the “−CYCLE” andFIG. 8C corresponds to the extreme of the “+CYCLE” while FIG. 8B showsthe equilibrium position for this unbiased bearing element. In each ofthese figures, the bearing element 100 is comprised of a piezoelectrictransducer of thickness Z₀ and is attached to a compliant base supportmember region 67 on the base member 92-2 with a cylindrical supportmember 66-1. FIGS. 8D to 8F however, show the same bearing element 100with a high voltage applied from either the cross section controllingmeans or the bias (both not shown, but see FIG. 7A) which increases thethickness by ΔZ_(BE) along the length. With no force applied, asillustrated, ΔZ_(BE) has a value of ΔZ_(M). For clarity of illustration,the magnitude of these microscopic expansions and contractions in FIGS.SA to 8F have been greatly exaggerated.

[0155] This drive electronics package is not just limited to drivingdirect-drive bearings, but can be reconfigured, as illustrated by FIG.7B, to the electronics package 501 for the case of indirect-drivebearings which use a piezoelectric transducer as an extension member.When this configuration is used, the output of the adjustable highvoltage supply 326 is connected directly to the upper extension memberelectrode surface 178U through the upper wire 75U instead of beingsummed with the signal from the excitation driver 316 and the lower wire75L attached to the lower extension member electrode surface 178L isheld at a fixed potential. This adjustable high voltage supply 326 willthen produce its own electric field, E₂ to interact with the dipolemoment, P₂ in the extension member while the field, E₁ is produced inthe transducer by the signal from the summing unit 324 to interact withthe dipole moment, P₁.

[0156] To further illustrate the use of the drive option of FIG. 7B, thebearing element embodiment of FIG. 9A has been provided which shows anadditional piezoelectric device being used as a two-half wavelengthextension member 78-5. This extension member 78-5 has an upper 78U and alower 78L electrode connected to the electronics package 501 by thewires 75U and 75L respectively.

[0157] An alternative use for the drive option of FIG. 7B is the casewhere a direct-drive bearing element Q is not large enough to sustainthe required oscillation level with a peak-to-peak oscillating voltagesafely below the electrical breakdown voltage when driven with theelectronics package of FIG. 7A. For this case, an alternative basemember configuration, such as depicted in FIG. 9B, can be used. Asillustrated, the base member 92-4 is a piezoelectric device whose upper92U and lower 92L electrodes are connected to the electronics package501 by the wires 75U and 75L respectively, so that the bearing'sdimension in the Z-axis can be adjusted.

[0158] The electronics package 500 of FIG. 7A can also be transformed byone skilled in the art, to drive, in a similar fashion, a transducercomprising of a core of magnetostrictive material 69M (see FIGS. 4B and5B). In this case, the output from the summing unit 324 would drive amagnetic excitation coil wound around the core so that a magnetic fieldB can be generated in the material to produce a mechanical dimensionalchange. Alternatively, because magnetic fields can be superimposed inthe core material itself, the output from the excitation driver 316 canbe summed with the adjustable high voltage supply 326 and connecteddirectly to one side of an excitation coil with the other side of theexcitation coil used as input to the converter 304 while the bias means330 and its ground reference can connect directly to a separatepolarization coil wound around the same core or placed externally to thedevice.

[0159]FIG. 10 shows the general relationship between the various majormechanical components of a sonic bearing along with the forces actingthereon. The applied force or simply referred to as the force F_(APP) 45, has a normal component [F_(APP)]_(Z), 44 directed along the Z-axis,which is used to press the load member 84-3, the bearing element 100 andthe base member 92-3 together such that all the appropriate slidingsurfaces and regions of each component are in direct contact. It must benoted that the force used to press the load member 84-3, the bearingelement 100 and the base member 9-23 together can be generated bycompression, tension, shear, or any combination thereof. The bearingelement 100 is mechanically connected to the base member 92-3 at thebase support member region 67 by a cylindrical support member 66-1 atthe nodal region on the bearing support region 65, using an adhesivemeans.

[0160] The force F_(APP) 45, can be generated by any mechanism such asgravitational, electric, magnetic and electromagnetic fields, or othermechanical structures, but is typically a load force F_(LOAD) containinga gravitational force F_(MG) representing the weight of the load memberand an external force F_(EXT) generated by an external source. TheZ-axis component [F_(LOAD)]_(Z), 43 of the load force F_(LOAD),therefore has the Z-axis components [F_(MG)]_(Z), 42 and [F_(EXT)]_(Z),41 of the load force F_(LOAD), force respectively. Later, the forceF_(APP) will be shown to include a bearing element generated forceF_(BE), having a Z-axis component [F_(BE)]_(Z), 40 for use in amulti-bearing element force servo mechanism to alter the bearing'sintrinsic stiffness.

[0161] Still in reference to FIG. 10, the resonant microscopicvibrational motion (not shown) of the bearing element 100 activated bythe excitation driver of the electronics package 500 are parallel to theY-axis. A applied sliding force 46 can be applied to the load member84-3 to initiate and maintain a load sliding motion in the XY-planealong the directions 48-2. This sliding force is usually derived from amotor, an actuator, a piston, a gear train, a leadscrew, a manual meansor some combination thereof, but can also be the result of the X-axialor Y-axial components of the force F_(APP) 45.

Results

[0162]FIG. 11A shows the sonic bearing assembly's effective coefficientof friction, μ_(SB) as a function of the bearing element's contact padr.m.s. velocity, ν_(SB) ^(rms) for the case when the load slidingvelocity, ν_(LOAD) is much less than ν_(SB) ^(rms). All the measurementswere taken using the sonic bearing assembly configuration shown in FIG.10. For each velocity, ν_(SB) ^(rms), the μ_(SB) is determined bymeasuring the magnitude of the minimum applied sliding force required tomove the load divided by magnitude of the normally directed component[F_(APP)]_(Z) of the force F_(APP). The velocities of the oscillatingcontact pad surfaces are measured by using a focused HeNe laser beambouncing off a very small and thin silicon cantilever onto an opticalsplit detector. One end of the cantilever is attached to a fixed basewhile the other end is glued to the vibrating bearing element near acontact pad surface. The r.m.s. velocity at the contact pad surfaces isproportional to the measured vibrational amplitude divided by theoscillation period. A single point calibration of the proportionalityconstant is obtained by translating the bearing element by a known tenmicron distance using a DM-13 submicron resolution differentialmicrometer from Newport Corp. Irvine, Calif., and measuring theresulting changes in the signal amplitude on the split detector.

[0163] Historically, it is well known from numerous brake, clutch andpiston seal studies that for many materials, the coefficient of kineticfriction μ_(k) decreases with increasing sliding velocities in the 0 to10 m/sec range. To demonstrate that the observed effect of the sonicbearing's apparent reduction of the effective coefficient of friction isnot simply a reduction of the actual coefficient of kinetic friction dueto the r.m.s. velocity of the contact pad members, the experimentalμ_(k) for tungsten carbide sliding against an unlubricated tungstencarbide is obtained in the velocity range of interest. FIG. 11B showsthe μ_(k) for an acetone cleaned and polished ISO M20 grade tungstencarbide rod sliding against a stationary, flat ISO M20 grade tungstencarbide plate. The μ_(k) value for a given sliding velocity is derivedby dividing the measured magnitude of the friction generated tangentialforce on the flat plate by the magnitude of the normal component of theforce F_(APP). From the data presented in FIG. 11B, it is clear that forunlubricated tungsten carbide sliding on tungsten carbide, μ_(k) indeeddecreases with increasing velocities, but not at the rate ofapproximately inverse velocity (i.e., 1/ν_(SB) ^(rms)) of the sonicbearing effect as depicted in FIG. 11A. The accuracy of the coefficientof friction measurements for the sonic bearing and the direct slidingsystems can be evaluated by comparing the μ_(SB) and μ_(k) values atzero sonic bearing oscillation level and at near zero rod/plate's linearsliding velocity respectively. The measured sonic bearing μ_(SB) (whenv_(SB) ^(rms)=0) value should theoretically be equal to the measuredμ_(k) (at v=0) value under these two limiting conditions.

[0164] One of the key features of the sonic bearing effect according toour interpretation of the adhesion theory is the ability to change theeffective coefficient of friction of the bearing without actuallychanging the actual coefficient of kinetic friction μ_(k) of the slidingsurfaces themselves. This is, of course done by externally supplyingmost of the energy which is dissipated by the frictional forces. FIG.11A clearly shows this decrease in apparent friction over and above thesmall decrease in the kinetic friction μ_(k) (see FIG. 11B) due only tothe velocity effect. By measuring the power consumption profile of thesonic bearing at various bearing r.m.s. velocities, it will be possibleto determine if the observed decrease in bearing friction is due to (1)the sonic bearing effect where the actual coefficient of kineticfriction μ_(k) of the sliding surfaces is nearly independent ofvelocity, or (2) an actual inverse velocity-like decrease in thecoefficient of kinetic friction μ_(k) of the sliding surfaces.

[0165] If the first hypothesis is valid, then the electrical powerconsumption profile of the sonic bearing due only to an external loadshould be initially linearly proportional to the bearing's r.m.s.velocity ν_(SB) ^(rms). This is because the bearing's power dissipationis equal to the product Of μ_(k), the magnitude of the normal componentof the force F_(APP), and the velocity parameters. Since the μ_(k) fortungsten carbide sliding against tungsten carbide is nearly constant atlow velocities (see FIG. 11B), the load power dissipation shouldtherefore also be linear with velocity and as the bearing velocityincreases, μ_(k) should decrease due to its slight velocity dependence,hence the expected power dissipation should deviate less than linear.

[0166] On the other hand, if the actual coefficient of kinetic frictionμ_(k) of the sliding surfaces is decreasing and this is the “real” causeof the sonic bearing's observed decrease in effective coefficient offriction μ_(SB) as shown in FIG. 11A, then the power consumption due toa given external load will not increase linearly with increasingvelocity ν_(SB) ^(rms). Specifically, if the friction between thesliding surfaces is decreasing as the inverse of velocity ν_(SB) ^(rms),as one may argue from the experimental effective coefficient of frictiondata of FIG. 11A, then the sonic bearing's power consumption profileshould be approximately constant and independent of the velocity ν_(SB)^(rms). This is because the power consumption is the product of themagnitude of the normal component of the force F_(APP), which isconstant, μ^(k), which is now assumed to vary inversely with velocity,and the velocity ν^(SB) ^(rms).

[0167]FIG. 12A shows the experimental data of the sonic bearing's loadr.m.s. power consumption, due to frictional sliding, as a function ofthe contact pad surfaces' r.m.s. velocity ν_(SB) ^(rms) using a fixed0.5 kgF force [F_(APP)]_(Z). The sonic bearing used in these experimentsemploys a bearing element which is similar to the one shown in FIG. 5Abut, the extension member and the contact pad members are entirely madefrom a single piece of tungsten carbide.

[0168] The data for the r.m.s. load power dissipation due to frictionalsliding shown in FIG. 12A was obtained by measuring the differences inthe sonic bearing's r.m.s. power consumption with and without the 0.5kgF force [F_(APP)]_(Z), on the bearing's load accepting surface. Withthe force, the power consumption is a combination of both internal andfrictional dissipation and without the force, the power consumption issimply the internal bearing dissipation. The solid line is the linearleast-square-fit to the experimental data in the low r.m.s. velocityν_(SB) ^(rms)domain while the dashed line shows the deviation of the rawdata away from linearity in the higher velocity region. As expected, atthe higher r.m.s. velocities of the contact pad surfaces, the powerdissipation should be slightly less than linear due to the slightdecrease in the μ_(k) value of the tungsten carbide sliding surfaces asshown in FIG. 11B.

[0169] In conclusion, the experimental power consumption data for thesonic bearing is fully consistent with the first hypothesis, where theactual coefficient of kinetic friction μ_(k) of the sliding surfaces ofthe bearing exhibits the normal unaltered characteristics shown in FIG.11B while at the same time, the sonic bearing exhibits a marked decreasein its effective coefficient of friction μ_(SB) as illustrated in FIG.11A.

[0170]FIG. 12B shows the experimental data of the sonic bearing'sinternal r.m.s. power dissipation as a function of the r.m.s. velocityν_(SB) ^(rms). The solid line is the quadratic nonlinearleast-square-fit to the experimental data. Note that the internal powerdissipation goes as the square of the velocity while the external loaddissipation increases only linearly with velocity ν_(SB) ^(rms). It isclear from the experimental data that the sonic bearing's ability todecrease the effective coefficient of friction μ_(SB) is most directlylimited by the internal power dissipation of the piezoelectrictransducer.

[0171] A unique method of improving the performance of the sonicbearing, as mentioned earlier, is to use an acoustic horn to convert thelow velocity transducer oscillations into high velocity motions at thecontact pad surfaces to achieve a low effective coefficient of frictionμ_(SB). For example, if the horn can amplify the velocity of thetransducer's displacement by only a factor of three, the internal powerdissipation of the transducer can be reduced by nearly a factor of nine.

[0172]FIG. 13A shows the experimental setup used to measure theeffective coefficient of friction μ_(SB) of a sonic bearing in both theactive (i.e., ON, ν_(SB) ^(rms)≈1 m/s) and inactive (i.e., OFF, ν_(SB)^(rms)≈0 m/s) states as a function of the bearing's sliding path angleθ. This experiment is designed to test the adhesion theory's predictionthat the severance of the chemical bonds between the bearing element 100and the load member 84-4 due to the microscopic oscillatory slidingmotions of the bearing element's contact pad surfaces, releases thebearing element 100 and the nodally attached load to move as a singleunit in any path that is slidable on the planar load sliding surface184-4 of the load member 84-4. Mechanical constraints (not shown) havebeen implemented in this experiment to have the oscillatory slidingmotion of the bearing element 100 always be parallel to the Y-axis,while the load member/bearing element unit can slidably translate at anyangle θ with respect to the Y-axis.

[0173]FIG. 13B shows the experimental data of the effective coefficientof friction as a function of the sliding path angle θ with and withoutthe bearing element oscillating (i.e., ON and OFF, respectively). Aspredicted by adhesion theory, the effective frictional properties of thesonic bearing are substantially independent of the sliding path angle θ.

[0174]FIG. 14A is the experimental setup used to determine therelationship between the Z-axial component [F_(APP)]_(Z), 44 of theforce F_(APP) on an oscillating bearing element 100 and the value of theforce output signal which represents the normal component of the forceF_(APP). As mentioned earlier, each sonic bearing element can also beused as an ultrastiff sensing means for the normal or vertical component[F_(APP)]_(Z), 44 of the force, F_(APP) 45 acting thereon. Most commonforce sensors operate according to the spring equation where the appliedforce on a spring-like device is equal to the measured deflection ofthat device times its spring constant. The force sensing mechanism ofsonic bearings does not use compressive deflection for the sake ofmaintaining extremely high bearing compressive stiffness. Instead, sonicbearing devices use frictional power dissipation in conjunction withmaintaining a constant oscillation level to determine the force[F_(APP)]_(Z) and from that, generate a “force output signal.”

[0175] To see how this ultrastiff force sensing mechanism operates, weneed to calculate the frictional power loss in the contact pad surfacesof the bearing element 100 over one cycle of oscillation. The frictionalpower loss is given by the proportionality

frictional power loss˜μ_(k)[F_(APP)]_(Z)ΔYω_(SB);

[0176] where μ_(k) is the actual coefficient of friction of the twosliding surfaces, [F_(APP)]_(Z) 44 is the Z-axis component of the forceF_(APP) 45, ΔY is the oscillation sliding distance over one-half cycle,and ω_(SB), is the oscillation angular frequency of sonic bearing. Forclarity of illustration, the magnitude of these microscopic expansionsand contractions ΔY, have been greatly exaggerated. An electrical methodof determining the same frictional power loss in the contact padsurfaces is to calculate the r.m.s. value of the measured current, i andmultiply it by the change in the peak square wave drive voltage ΔV_(ω)on the piezoelectric transducer with and without the application of theforce F_(APP).

[0177] Therefore, equating the two power calculations, we have

(i)(ΔV_(ω))˜μ_(k)[F_(APP)]_(Z)ΔYω_(SB);

ΔV_(ω)˜μ_(k)[F_(APP)]_(Z)ΔYω_(SB)/i.

[0178] For a given physical sonic bearing with a specific oscillationlevel setting in the electronics package 500, the parameters μk, ΔY,ω_(SB) and i are all fixed constants, we therefore have

ΔV_(ω)=(some constant)[F_(APP)]_(Z); or the inverse,

[F_(APP)]_(Z)=(lisome constant)(ΔV_(ω)).

[0179] And, since the control unit 310 of FIG. 7A is designed to producea force output signal proportional to ΔV_(ω), we can arrive at theexpression

[F_(APP)]_(Z)=(constant)(Force Output Signal).

[0180]FIG. 14B is an experimental plot of the Z-axis component[F_(APP)]_(Z) of the force F_(APP) on a specific bearing element 100versus the “force output signal” generated by the electronics package500 illustration of FIG. 14A. The “force output signal” data was takenin response to an increasing force Z-axis component [F_(APP)]_(Z) on thebearing element. The slope of the linear least-square-fit curve is thecalibration constant.

Additional Embodiments

[0181] An important and preferred practical characteristic of a sonicbearing is the ability to always operate it in the ultrasonic frequencyrange. This frequency criterion is important because ultrasonicfrequencies are generally inaudible to humans. In the preferredembodiments described above, there is an inverse relationship betweenthe bearing's length and its operating frequency. For example, if thebearing element's size increases by a factor of three, the correspondinglowest operating frequency for that bearing will decrease by the samefactor of three. This reduction of the operating frequency may transformthe original ultrasonic frequency down into the audio range.

[0182] The embodiments shown in FIGS. 15A, 15B, and 15C are specificallydesigned to solve this lowering of the operating frequency problemassociated with large sonic bearings. The simplest, and therefore themost straightforward solution to this problem is to oscillate the largebearing element, not at its fundamental frequency, but rather at one ofits higher harmonic frequencies. In the example shown in FIG. 15A, alarge direct-drive sonic bearing element is excited by the electronicspackage 500 to operate at three times its fundamental frequency or itsthird harmonic. In the embodiments shown in FIGS. 15A and 15B, thebearing element comprises 3 transducers aligned in succession. Underthese conditions, there are a total of three, one-half wave segments(3λ/2) along the full length (i.e., parallel to the Y-axis) of thebearing element, containing a total of three nodal support regions (notshown) for attaching at least one cylindrical support member 66-1thereto, on the lower electrode surface 168L. Each nodal support is usedboth to establish oscillation boundary conditions and to attach thebearing element to the fixed base member 92-5. On the upper and lowerelectrode surfaces, there are two sets of eight upper 70U and lower 70Lcontact pad members with their respective upper 170U and lower 170L (notshown) contact pad surfaces. The moveable load member 84-5 has a loadaccepting surface 284-S and a sliding path direction 48-2, where theload sliding surface 184-S slides against the eight upper contact padsurfaces 170U of the bearing sliding surface.

[0183] A major problem with the 3λ/2 oscillation mode when used inconjunction with the configuration shown in FIG. 15A, is that duringresonance, the two end, one-third length sections of the bearing elementare always moving in a direction opposite to the piezoelectric inducedmovements, resulting in a two-third reduction of the electromechanicalcoupling efficiency κ₃₁ for that bearing element.

[0184] A solution to the low κ₃₁ coupling efficiency problem isillustrated in FIG. 15B and is based upon the electrical segmentation ofthe original continuous transducer's upper and lower electrode surfacesinto three equal electrode segment pairs labeled as: the upper 683U andlower 683L (not shown) left end-segment surfaces; the upper 682U andlower 682L (not shown) mid-segment surfaces; and the upper 681U andlower 681L (not shown) right end-segment surfaces. The electricalexcitation polarity for the two newly formed end-segment electrode pairs(681U, 681L), (683U, 683L) can now be reversed with respect to themid-segment (682U, 682L), so that for all three segments, thepiezoelectric forces are now in phase with the resonant oscillatorymovements. The changes in the two end-segment polarities are visuallyindicated in FIG. 15B by the two “−” signs and the direction of theelectric field, E with respect to the piezoelectric material's uniformelectric dipole moment direction, P. The wires connected to each of thethree electrode segment surfaces of the modified transducer have beenappropriately labeled so that all the excitation wires tagged as 74U areconnected together and similarly, the three excitation wires labeled as74L are connected together. The modified transducer is attached to thebase member 92-5 using three cylindrical support members 66-1. The uppertransducer face is now a collection of the three separate areas ofelectrodes 681U, 682U and 683U. Like the design in FIG. 15A, themoveable load member 84-5 has a load accepting surface 284-5 and aplanar load sliding surface 184-5 for sliding along any path in thedirection 48-2.

[0185] A totally different approach to extending the length of a sonicbearing without changing its operating frequency is illustrated in FIG.15C. This technique uses the indirect-drive bearing element, where thepiezoelectric transducer is always driven at its lowest longitudinalfrequency mode, while the extension member is resonated at one of itshigher harmonic frequencies. Because the transducer is operated at itsfundamental mode, the electromechanical coupling coefficient κ₃₁ isalready optimized without engaging in the labor intensive transducerelectrode modifications used in FIG. 15B. Furthermore, if the materialfor the extension member is selected to have a high quality factor Q athigh frequency, then resonating the extension member at one of itshigher harmonics will exhibit no substantial loss in acoustic energies.

[0186]FIG. 15C shows a specific example of an embodiment where thebar-shaped 3λ/2 extension member 78-3 is operated in the 3λ/2 mode andthe material is ISO M20 grade tungsten carbide measuring approximately145 mm in length by 13.1 mm wide by 5.15 mm thick. The C5800piezoelectric transducer from Channel Industries Inc., Santa BarbaraCalif., is operated in the λ/2 mode and has dimensions of 25.3 mm longby 13.1 mm wide by 6.75 mm thick. Like the direct-drive bearing elementsshown in FIGS. 15A and 15B, there are also three extension member nodalregions (not shown) and their three associated cylindrical supportmembers 66-2 located geometrically at the same relative positions to thecontact pad members as in the direct-drive cases. These cylindricalsupport members 66-2 are also used to establish the boundary conditionsand to affix the 3λ/2 extension member 78-3 to the base member 92-6. Asingle transducer nodal region on the lower electrode surface 168L (notshown), which is oppositely facing the upper electrode surface 168U isused to attach the transducer's cylindrical support member 66-1 to thesame base member 92-6. The resonant frequencies for both the transducerand the third harmonic driven extension member are approximately equalto 67 kHz. The two extension member's surfaces parallel to the XY-planeof the extension member body 578-3 are upper and lower extension memberfaces. The precise resonant frequency of the extension member is ofcourse, dependent on the sizes and placements of the eight upper 70U andeight lower 70L contact pad members on the extension member faces. Theassociated eight upper contact pad surfaces 170U of the bearing slidingsurface are used to slide against a single planar load sliding surface184-6. The long moveable load member 84-6, having a load acceptingsurface 284-6, for the sonic bearing in FIG. 15C is shown in twoalternate positions to indicate a possible translational movements inthe XY-plane along 48-2.

[0187] The shape of the bearing sliding surface or bearing supportregion can also be altered to perform useful functions. For example,FIG. 16 shows a direct-drive, λ/2 mode, sonic bearing designed tosupport a rod-shaped, rather than a bar-shaped, load member 84-7 whichis capable of both translational 48-1 and rotational 48-3 directions ofmotion. The four contact pad members 71U on the upper electrode surface168U have been specially modified to have complementary mating surfacesto the load member's load sliding surface 184-7. The four contact padsurfaces 170L (not shown) of the bearing support region can still retaintheir original plate-shaped form and slide against the planar basesliding region 192-7 of the base member 92-7. For clarity ofillustration reasons, the front part of the load member 84-7 has beensectioned and moved forward to reveal the cylindrically concave shape ofthe upper contact pad surfaces 171U on the upper contact pad members71U.

[0188] An important extension is a multi-bearing element sonic bearingassembly using more than one sonic bearing element in contact with theload and base members. This sonic bearing assembly can have both directand indirect-drive versions. FIGS. 17, 18, and 19 depict simplifiedultrastiff direct-drive embodiments using two bearing elements. Theseembodiments share many similarities with the planar embodiment of FIG.6A which uses only one bearing element. However, the embodiments ofFIGS. 17, 18, and 19 take advantage of three major aspects of theinvention, namely: (1) the sonic bearing effect, (2) the cross sectioncontrolling means, and (3) the force sensing mechanism.

[0189] Ordinarily, because the type of assembly depicted in FIGS. 17,18, and 19, confines the load member 84-10 in one of the two axes (i.e.,X-axis or Z-axis ) orthogonal to the axis of the load sliding motion(i.e., Y-axis), a zero tolerance condition in the manufacturing of theparts for the assembly must be maintained along this axis ofconfinement, which, for the examples of FIGS. 17, 18, and 19, is theZ-axis. Furthermore, when all contact pad surfaces are not parallel tothe direction of the load sliding motion and are in continuous contactwith the load member or if the load member should undergo some kind ofdimensional change (e.g., thermal expansion), it is the force F_(APP) aswell as the slidable path that will be modified as the load memberslides.

[0190] In order to avoid the undesirable effects of these aforesaidconditions the sonic bearing assemblies illustrated in FIGS. 17, 18, and19, instead, take advantage of this fact of confinement. Because onebearing element in these embodiments is symmetrically positioned to beopposite the another and because conventional manufacturing tolerancesas well as any thermal induced material changes just happen to be withinthe range of bearing element thickness control, a very simple “forceservo mechanism” can be used to compensate for most mechanical orthermal variations. This force servo mechanism is accomplished in theembodiments of FIGS. 17 and 18 by using the “force sensor output” signalfrom one electronics package 500 generated from the force sensingmechanism of one bearing element as the “force servo input” signal tothe cross section controlling means of another electronics package 500for the opposite bearing element. The end result is that a constantforce in the Z-axis [F_(APP)]_(Z), 44 ( not shown, but see FIG. 10) ismaintained on one bearing element 100 as the load member 84-10 slidesalong the slidable path direction 48-1. This force, [F_(APP)]_(Z) isheld constant because the feedback produces a change in the value ofV_(HV) which, when conveyed by the wires to the opposite bearing element100 along with the square wave excitation voltage V_(ω), will produce athickness change therein.

[0191] For the embodiment of FIG. 19, the force servo mechanism isrealized by connecting the “force servo input” for one bearing elementto the “force sensor output” of the other and vice versa, so that, withsome minor control loop modifications, the dynamic range of stiffnesscompensation for the bearing assembly can be substantially increased.

[0192] FIGS. 20 to 22 illustrate three different states of the bearingassembly of FIG. 17 reflecting a change in the thickness of the loadmember 84-10 brought on by thermal expansion and contraction while thedimensions of the base member 92-10 and the bearing elements 100 arehere assumed to be independent of temperature. For clarity ofillustration, the magnitude of these microscopic expansions andcontractions have been greatly exaggerated. The state in FIG. 21corresponds to the initial assembled state of the bearing assemblybefore the occurrence of any thermal expansion or contraction. In thisstate, a mechanical prebias from the C-shaped base member 92-10 incooperation with the electronics package 500 designated by E.P. #2supplying a voltage VHV₂ with a value of V₀ sets the initial thickness(Z₀-ΔZ₀) of the upper bearing element 100. This initial upper bearingelement thickness generates a bearing element force F_(BE2), having aZ-axis component [F_(BE)]_(Z), 40 (not shown, but see FIG. 10) whichwhen combined by vector addition with any load force F_(LOAD) with aZ-axis component [F_(LOAD)]_(Z), 43 (not shown, but see FIG. 10) on theload member 84-10, establishes a force F_(APP) with a Z-axis component[F_(APP)]_(Z) 44 (not shown, but see FIG. 10) on the lower bearingelement 100 according to

F _(APP) =F _(BE2) +F _(LOAD).

[0193] Normally, the load force F_(LOAD) is composed of two vectorcomponents; a gravitational force representing the mass of the loadmember under the pull of gravity F_(MG) (having a Z-axis component[F_(MG)]_(Z), 42 not shown here, but see FIG. 10) and any external forceF_(EXT) having a Z-axis component [F_(EXT)]_(Z), 41 not shown here, butsee FIG. 10) summed together again by vector addition to produce

F _(LOAD) =F _(MG) +F _(EXT).

[0194] However, in this simple illustration, the magnitude of theexternal force F_(EXT) is set to zero and the force F_(MG) is assumed tohave a constant magnitude and is directed along the Z-axis.

[0195] At this point, if a dimensional change occurs to the load member84-10 along the axis of confinement (i.e., Z-axis) which attempts toalter the force component [F_(APP)]_(Z), as illustrated by the α statein FIG. 20 and β state in FIG. 22, the electronic force servo mechanismwill change the value of V_(HV2) to produce a corresponding thicknesschange ΔZ_(BE2) of either ΔZ_(α) or ΔZ_(β) respectively, in the upperbearing element 100 in order to maintain the magnitude and direction ofthe force component [F_(APP)]_(Z) to be the same constant value as inthe initial state of FIG. 21. In this way, the slidable path along thelower bearing element is preserved.

[0196] The operational principle of the force servo mechanism is basedon the graphs depicted in FIGS. 23A and 23B which describe the magnitudeof the Z-axis component [F_(BE)]_(Z) of the bearing element generatedforce F_(BE2) as a function of both the bearing element thicknessdisplacement ΔZ_(BE2) and the applied high voltage V_(HV2). Theseparticular graphs are for a piezoelectric transducer, but these types offunctional relationships are well known in the art for mostelectromechanical transducers and are described by the equation

[F _(BE)]_(Z)=(k _(BE))(d ₃₃)(V _(HV))−(k _(BE))(ΔZ _(BE));

[0197] where the equivalent spring constant k_(BE) of the bearingelement 100 (not shown, but see FIG. 17) is given by

k _(BE)=(A _(BE))(Y _(BE))/Z ₀.

[0198] Here A_(BE) is the total area at the interface of the bearingelement, Y_(BE) is the short circuit Young's modulus Y₃₃ ^(E) of thepiezoelectric transducer of the bearing element along the Z-axis, d₃₃ isthe piezoelectric charge constant in the thickness direction and Z₀ isthe initial thickness of the transducer before the application of anyforces and/or voltages.

[0199] The purpose of the force servo mechanism, in reference to FIGS.20 to 22, is to change the value of the quasi-DC high voltage V_(HV2)applied to the upper bearing element 100 so as to change its thicknessdisplacement value ΔZ_(BE2) in order to maintain a constant magnitudeand direction of the force component [F_(APP)]_(Z) on the lower bearingelement 100. The particular value of V_(HV2) required for each state(i.e., for ΔZ_(α), ΔZ₀, and ΔZ_(β)) is obtained, in a graphic sense,according to FIG. 23A, by the trinary intersection of the horizontalline where [F_(BE2)]_(Z) has a value equal to F₀, with the vertical linerepresenting the required displacement value ΔZ_(BE2), with the diagonalline relating the behavior of [F_(BE2)]_(Z) versus ΔZ for a given valueof V_(HV2). The horizontal line at F₀ has a value equal to the Z-axismagnitude value of F_(APP) minus F_(LOAD) and is used because the forcecomponent [F_(BE2)]_(Z) generated by the upper bearing element 100required to maintain a constant force component [F_(APP)]_(Z) on thelower bearing element for the states shown in FIGS. 20, 21 and 22, issimply given by the Z-axis magnitude value of F_(APP) minus F_(LOAD).Here, also, as previously mentioned, the Z-axis magnitude value ofF_(LOAD) is assumed to only be the magnitude value of F_(MG) (i.e., noexternal force F_(EXT) on the load member). Therefore, to changeΔZ_(BE2) from ΔZ_(α) to ΔZ_(β), the quasi-DC high voltage V_(HV2) mustchange between V_(α) and V_(β) respectively, in order to insure that,[F_(APP)]_(Z) will remain constant.

[0200] Alternately, as illustrated in FIG. 23B, when an external forceF_(EXT) is applied to load member 84-10 (not shown, but see FIG. 17),while all the mechanical dimensions of the bearing system are nowassumed to be fixed, the force servo mechanism must change the value ofthe quasi-DC high voltage V_(HV2) applied to the upper bearing element100 (not shown, but see FIG. 17) so that the bearing element generatedforce [F_(BE2)]_(Z) from the upper bearing element 100 (not shown) willchange in order to keep the force component [F_(APP)]_(Z) constant.Graphically speaking, as an increasingly larger external force's normalcomponent [F_(EXT)]_(Z) is applied, the trinary intersection point willmove down along the line of constant ΔZ_(BE2) (i.e., along ΔZ₀) as theforce servo mechanism drops the value of the quasi-DC high voltageV_(HV2) from V₀ to V_(N). This causes the bearing element generatedforce's normal component [F_(BE2)]_(Z) to drop in value from F₀ to zerowhich compensates exactly for the applied external force's normal[F_(EXT)]_(Z). For the purpose of illustration, at the point where thevalue of [F_(EXT)]_(Z) is equal to one-half of F₀, the high voltageV_(HV2) is shown to have an approximate value of one-half the quantity(V₀-V_(N)). Below the value of V_(N), the force servo mechanism will nolonger function because this region represents a physical separation ofthe upper sliding surfaces of the upper bearing element 100 (not shown)from the load sliding surfaces of the load member 84-10 (not shown).

[0201] In actual operation, the exact value of the quasi-DC high voltageV_(HV2) generated as a result of the force servo mechanism, and hence,the trinary intersection point, will be graphically determined by acombination of both graphs in FIGS. 23A and 23B because components ofthe bearing assembly will usually experience a thermally induceddimensional change when an external force F_(EXT) is present.

[0202] A detailed graphic description of the operation of the forceservo mechanism for the embodiment of FIG. 17 subject to an arbitraryapplied external force is illustrated in FIGS. 24A to 24C. FIG. 24Ashows how the force servo mechanism changes the values of V_(HV2) and,consequently, [F_(BE2)]_(Z) when an external force F_(EXT) is appliedwith a component along the Z-axis. The value of F₀ is chosen as thevalue of the servo equilibrium bearing element force's normal component[F_(BE2)]_(Z) as a result of the application of the voltage V_(HV2)equal to V₀ for the upper bearing element (not shown, but see FIG. 17).From this point, a change in the external force's normal component[F_(EXT)]_(Z) is directly compensated for by a change in [F_(BE2)]_(Z)in order to maintain the normal component [F_(APP)]_(Z) on the lowerbearing element (not shown, but see FIG. 17) constant as shown in FIG.24B. Because [F_(APP)]_(Z) is held constant by the force servomechanism, the lower bearing element thickness (Z₀ 30 ΔZ_(BE1)), andhence, the slidable path thereon will be preserved in the servo regionas shown in FIG. 24C.

[0203] For this servo configuration of FIG. 17, the region of enhancedstiffness as depicted in FIG. 24C can be shifted by adjusting the valueof F₀. In order to maximize the range of load carrying capability for anexternal force F_(EXT) directed on the lower bearing element, the valueof F₀ should be adjusted such that the magnitude of the normal forcecomponent [F_(APP)]_(Z) without an external force F_(EXT) is very nearto the maximum allowable value F_(M) for the force component[F_(APP)]_(Z). The value F_(M) represents the point where the velocitycontrol servo is just barely able to maintain the set r.m.s. velocity ofthe bearing element, and hence, the set level for the effectivecoefficient of friction μ_(SB). At this point, the value V₀ is equal tothe maximum servo value V_(M) that V_(HV2) is allowed to have. Theimportant ramification of choosing such a large F₀, other than the lowerbearing element being able to support a significant load withoutaltering the slidable path thereon, is that each bearing element's Q canbe lowered which will allow for an extremely short settling time and anextremely large locking force when the bearing elements are switched tothe “OFF” state.

[0204] In a similar fashion, the force servo mechanism for theembodiment of FIG.18 is graphically illustrated in FIGS. 25A to 25C. Themain difference of this servo configuration, illustrated in FIG. 18, isthat the upper bearing element's sliding surfaces define the slidablepath and the lower bearing element adjusts the force component[F_(APP)]_(Z) by changing th,e magnitude of the lower bearing elementgenerated force component [F_(BE1)]_(Z). For this configuration, F₀ canbe chosen as shown in FIG. 25A to be very near zero in order to againmaximize the range of load carrying capability for an external forceF_(EXT) directed on the lower bearing element. This results in thebearing elements maintaining their very high Q at low external forcevalues and thus, reduces the power requirements needed to overcome thefrictional power dissipation. Any degradation in settling time andlocking force for this embodiment can also be eliminated by settingV_(HV1) and V_(HV2) to V_(M) when the bearing assembly is switched tothe “OFF” state. In this way, the bearing element also acts as an activebrake.

[0205] For the embodiment of FIG. 19, each of the servo configurationsemployed in FIGS. 17 and 18 are used cooperatively to achieve a forceservo mechanism with an extended servo range. As graphically depicted inFIGS. 26A and 26B, the force component [F_(APP)]_(Z) on either bearingelement in the embodiment of FIG. 19 is selected to be equal to(F₀+F_(MG)) when no load force F_(LOAD) is applied and the magnitude ofthis force component [F_(APP)]_(Z) is near the value of F_(M). Selectingthe magnitude value of [F_(APP)]_(Z) near F_(M) as the initial conditionallows the portion of force servo mechanism configured like that of FIG.17 to handle a load force F_(LOAD) directed on the lower bearing elementwith maximum range while allowing the other portion of the force servomechanism configured like that of FIG. 18 to handle the load forceF_(LOAD) directed on the upper bearing element with maximum range. Inthis way, each portion of this cooperative servo mechanism operates onlyon its own side of a switching point defined at the point when themagnitude of F_(LOAD) equals zero. The graph of FIG. 26C shows thisswitching point and illustrates that the extended servo range is acombination of each range from each portion of this force servomechanism.

[0206] A further and final illustration which also takes advantage ofthe three aforementioned major aspects of the invention is theembodiment of FIG. 27. In this example, four bearing elements 100 aremounted to the base member 92-9. Specifically, the bearing supportregions, configured opposite of the bearing sliding surfaces, arejuxtaposed to each other along the inner faces of the base member 92-9.Also, the load sliding surfaces 86-9 of the rectangularly shaped loadmember 84-9 are juxtaposed to each other and are in slidable contactwith the bearing sliding surfaces along 48-1. This type of assemblyfurther confines the load member in both of the two axes (i.e., X-axisand Z-axis) orthogonal to the axis of the load sliding motion (i.e.,Y-axis) and can be implemented as an obvious extension using twoorthogonal versions of the embodiment of FIG. 19. For clarity ofillustration, the second set of two electronics packages and theirinterconnection to each other and their respective bearing elements arenot shown.

[0207] An important consequence and major advantage resulting from theuse of a force servo mechanism in a sonic bearing assembly is to enablethat assembly to have, not only the ability to maintain constantstiffness overtime, but also to have an adjustable stiffness. Thisability allows the assembly to possibly have a lower stiffness than theintrinsic bearing stiffness itself, but more importantly, the assemblycan emulate a bearing having nearly infinite stiffness. According to theprinciples of control theory, precise knowledge of systemcharacteristics are not required in order to achieve precise control.Therefore, simple servoed control over the force component [F_(APP)]_(Z)can make a bearing assembly substantially less sensitive to theparameters that attempt to alter that force component and it is thisservoed control that will directly manifest itself in a real increase inbearing stiffness over and above the intrinsic stiffness of a similarnon-servoed assembly. As mentioned for the embodiment of FIG. 17, theforce component [F_(APP)]_(Z) is maintained by the force servo mechanismaltering the value of [F_(BE2)]_(Z) in order to compensate for anychange in F_(LOAD). Typical simple servo mechanisms can easily providesteady-state compensation control to within 0.1 percent which translatesto a theoretical increase in bearing stiffness by 1000 times. And, ifcomplete models of the components in the bearing assembly itself areconsidered in a servo mechanism design, a robust dynamic stiffness ofthe same order can also be achieved. Therefore, using conventional servodesign methods, one skilled in the art can easily develop such amechanism that will provide both steady-state and transient highstiffness solutions required for smooth and precise motion while at thesame time, reject disturbances to the bearing stiffness.

Summary, Ramifications and Scope

[0208] Accordingly, the reader will see that a sonic bearing of theinvention is ideal for use in a very high stiffness precision stage usedfor guiding rectilinear or rotational motion. Specifically, a sonicbearing equipped stage can move a load with high precision to thedesignated coordinate by using the bearings in their “active” or lowfrictional state. After reaching the target position, the velocity ofboth the load and the stage can be rapidly and controllably decreased tominimize the settling time at the target position by transitioning thebearings into their “inactive” or high frictional state. Furthermore,because the bearing possesses the attribute of being able to alter itsthickness, any imprecision or change in mechanical tolerances that causea degradation in stiffness at any time can be easily eliminatedindependent of the frictional state of the bearing. In this manner, asonic bearing stage can simultaneously exhibit both high stiffness withlow effective friction and high precision with short settling time. And,after reaching the desired location, the stage can then be “locked” inplace with or without using any external power. It can also beappreciated that the sonic bearing has the additional advantages of:

[0209] providing high reliability;

[0210] providing excellent wear resistance;

[0211] providing low sensitivity to shock loading;

[0212] providing excellent off-axis error characteristics; and

[0213] providing for operation in many exotic environments.

[0214] Although the description above contains many specificities, theseshould not be construed as limiting the scope of the invention butmerely providing illustrations of some of the presently preferredembodiments of this invention.

[0215] For example, other possibilities may include sonic bearings whosebearing elements are planar but round rather than bar-shaped, or evennon-planar such as those having cylindrical, conical or spherical shapedgeometries. Thus, the scope of the invention should be determined by theappended claims and their legal equivalents, rather than by the examplesgiven.

We claim:
 1. A method of controlling an effective coefficient offriction between a first surface of a first element and a second surfaceof a second element, the method comprising the steps of: a. configuringthe first and second surfaces to be in slidable contact with one anotheralong an interface between the first surface and the second surface andunder a force sufficient to maintain contact and having a staticfriction therebetween; and b. inducing a repetitive motion in the firstsurface parallel to the interface thereby altering the effectivecoefficient of friction.
 2. A method of controlling an effectivecoefficient of friction between a first surface of a first element and asecond surface of a second element, the method comprising the steps of:a. configuring the first and second surfaces to be in slidable contactwith one another along an interface between the first surface and thesecond surface and under a force sufficient to maintain contact andhaving a static friction therebetween; and b. inducing a symmetricalmotion in the first surface parallel to the interface thereby alteringthe effective coefficient of friction.
 3. The method according to claim2 wherein the first element comprises a set of dimensions, the methodfurther comprising the step of varying a desired dimension of the firstelement in response to an electronic signal.
 4. The method as claimed inclaim 3 wherein the step of varying the desired dimension furthercomprises providing a transducer having the set of dimensions, thetransducer converting the electronic signal into microscopic mechanicaldisplacements to generate the symmetrical motion.
 5. The methodaccording to claim 4 further comprising generating the electronic signalat a predetermined frequency which in turn varies the desired dimensionat a corresponding velocity.
 6. The method as claimed in claim 5 furthercomprising the step of amplifying the mechanical displacements.
 7. Themethod as claimed in claim 6 wherein the step of amplifying furthercomprises producing a resonance in the transducer to amplify themechanical displacements by an amplification factor proportional to aquality factor.
 8. The method as claimed in claim 7 wherein the step ofproducing the resonance further comprises the steps of: a. determining alongitudinal acoustic resonant frequency of the transducer along thedesired dimension; and b. generating a frequency of motion in thetransducer substantially equal to the resonant frequency.
 9. The methodas claimed in claim 5 further comprising the step of providing at leastone extension member having an extension member body, the body beingattached to the transducer.
 10. The method as claimed in claim 9 furthercomprising the step of transferring the mechanical displacements to theextension member body.
 11. The method as claimed in claim 10 furthercomprising the step of making the corresponding velocity proportional toa gain factor of the extension member body.
 12. The method as claimed inclaim 2 further comprising the step of temporally nulling a plurality offrictional forces generated by the symmetrical motion along theinterface for at least one oscillation cycle by: a. maintaining theforce to be constant for the cycle; b. adapting the surfaces to have anactual coefficient of friction substantially uniform along any slidablepath; and c. providing the second element with a substantially largeinertial mass.
 13. The method as claimed in claim 2 further comprisingthe step of spatially nulling a plurality of frictional forces generatedby the symmetrical motion along the interface by selecting the interfacesuch that at least one frictional force from a region within theinterface is opposed by at least one substantially equal and oppositefrictional force from another region within the interface.
 14. Themethod as claimed in claim 2 further comprising the step of reducing anactual coefficient of friction between the first and second surfaces.15. The method as claimed in claim 14 wherein the step of reducing theactual coefficient of friction further comprises adding a lubricantbetween the first and the second surfaces.
 16. The method as claimed inclaim 14 wherein the step of reducing the actual coefficient of frictionfurther comprises applying a thin film of material of a predeterminedthickness to at least one of the surfaces.
 17. The method as claimed inclaim 16 further comprising the step of modifying the thin film by ionimplantation of a predetermined number of ions/cm².
 18. The method asclaimed in claim 2 further comprising the step of minimizing bondingbetween the first and the second surface.
 19. The method as claimed inclaim 18 wherein the step of minimizing the bonding further comprises:a. polishing at least one surface to a predetermined degree of flatnessper unit area; b. texturing at least one surface to form a series ofmicroscopic recesses in accordance with a controlled and reproduciblepattern; and c. coating at least one surface with an anti-bonding film.20. The method as claimed in claim 18 wherein the step of minimizing thebonding further comprises: a. limiting a contact pressure between thefirst and the second surface to be less than 1 MPa; b. controlling eachsliding surface to have a temperature between 0° C. and 50° C.; c.generating a frequency of the symmetrical motion of the first element ina range between 0 kHz and 120 kHz; and d. selecting the frequency of thesymmetrical motion to be a longitudinal acoustic resonant frequency ofthe first element.
 21. The method as claimed in claim 18 wherein thestep of minimizing the bonding further comprises: a. selecting a meltingtemperature of a surface material for each of the surfaces to besubstantially greater than 1000° C.; b. selecting a crystallinestructure of the first surface to be substantially different than acrystalline structure of the second surface; and c. selecting a thermalconductivity value of at least one surface to be large.
 22. The methodas claimed in claim 2 further comprising the steps of: a. determining aroot-mean-square velocity of the symmetrical motion of the first elementas a function along the first surface; b. determining a maximumroot-mean-square velocity of the motion of the first element along thefirst surface; and c. selecting a plurality of points in the firstsurface having the root-mean-square velocity within a predeterminedpercentage of the maximum root-mean-square velocity such that theselected points are configured to be in slidable contact with the secondsurface along the interface.
 23. The method as claimed in claim 2further comprising the step of initiating a sliding force to at leastone element such that the first element and second element move at atranslational speed relative to one another.
 24. The method as claimedin claim 23 further comprising the step of controlling aroot-mean-square velocity of the symmetrical motion in the first elementto be greater than the translational speed between the elements.
 25. Themethod as claimed in claim 2 further comprising the step or controllinga cross section of the first element to a predetermined specification.26. The method as claimed in claim 2 further comprising the steps of a.changing the force; b. generating a signal representing the change inforce wherein the signal is applied to a feedback mechanism; and c.controlling a cross section of the first element in response to thesignal from the feedback mechanism.
 27. The method as claimed in claim22 further comprising adapting one or more contact members to the firstelement at the selected points wherein the contact member is in slidablecontact with the second surface along the interface.
 28. A method ofcontrolling an effective coefficient of friction between a first surfaceof a first element and a second surface of a second element, the methodcomprising the steps of: a. providing at least two contact points on thefirst surface; b. configuring the contact points and the second surfaceto be in slidable contact with one another along an interface and undera force sufficient to maintain contact and having a static frictiontherebetween; and c. energizing the first element to repetitively andalternately expand and contract a physical dimension of the firstelement such that the contact points move away from and toward oneanother at a determined velocity and parallel to the interface therebyadjusting the effective coefficient of friction.
 29. The methodaccording to claim 28 wherein no substantial translational motion isimparted to the second element by energizing the first element.
 30. Themethod as claimed in claim 28 wherein the first element furthercomprises at least one transducer for converting electrical energy intomicroscopic mechanical displacements to generate the repetitive andalternative expansion and contraction at the determined velocity. 31.The method as claimed in claim 30 further comprising an excitation meansfor generating the electrical energy.
 32. The method as claimed in claim28 further comprising attaching at least one extension member to thefirst element, the extension member having an extension sliding surfaceand an extension member body with a variable cross section along adimension of the extension member body.
 33. The method as claimed inclaim 32 further comprising the step of amplifying the repetitive andalternative expansion and contraction of the first element.
 34. Themethod as claimed in claim 33 wherein the step of amplifying furthercomprises producing a resonance in the extension member, wherein therepetitive and alternative expansion and contraction is amplified by anamplification factor proportional to a quality factor of the extensionmember.
 35. The method as claimed in claim 34 wherein the step ofproducing the resonance further comprises the steps of: a. determining alongitudinal acoustic resonant frequency of the extension member alongthe dimension of the extension member body; and b. generating afrequency of motion in the extension member substantially equal to theresonant frequency.
 36. The method as claimed in claim 35 furthercomprising the step of transferring the amplified repetitive andalternative expansion and contraction of the first element to theextension sliding surface.
 37. The method as claimed in claim 32 furthercomprising the step of making the determined velocity proportional to again factor of the extension member body.
 38. The method as claimed inclaim 28 further comprising the step of temporally nulling a pluralityof frictional forces generated by the repetitive and alternativeexpansion and contraction of the first element along the interface forat least one oscillation cycle by: a. maintaining the force to beconstant for the cycle; b. adapting the surfaces to have an actualcoefficient of friction substantially uniform along any slidable path;and c. providing the second element with a substantially large inertialmass.
 39. The method as claimed in claim 28 further comprising the stepof spatially nulling a plurality of frictional forces generated by therepetitive and alternative expansion and contraction of the firstelement along the interface by: a. setting a frequency of the motion ofthe contact points; b. setting a phase of the motion of the contactpoints; c. setting an amplitude of the motion of the contact points; d.adapting the surfaces to have an actual coefficient of frictionsubstantially uniform along any slidable path; and e. selecting alocation of the contact points on the first surface such that at leastone frictional force from a region within the interface is opposed by atleast one substantially equal and opposite frictional force from anotherregion within the interface.
 40. The method as claimed in claim 39wherein the steps of setting the phase, frequency, and amplitude for themotion of the contact points further comprise: a. determining a commonresonant frequency, an individual resonant phase, and an individualresonant amplitude for the motion of the contact points resulting from asubstantially sinusoidal longitudinal acoustic resonant wave in thefirst element, whereby a propagation direction of the resonant wave isaligned substantially parallel to the first surface; b. setting thefrequency of the motion to be the resonant frequency; c. setting thephase to the resonant phase for the point; and d. setting the amplitudeto the resonant amplitude for the point.
 41. The method as claimed inclaim 28 further comprising the step of reducing an actual coefficientof friction between a contact point surface of the contact points andthe second surface.
 42. The method as claimed in claim 41 wherein thestep of reducing the actual coefficient of friction further comprisesadding a lubricant between the contact point surface and the secondsurface.
 43. The method as claimed in claim 41 wherein the step ofreducing the actual coefficient of friction further comprises applying athin film of material of a predetermined thickness to at least one ofthe surfaces.
 44. The method as claimed in claim 43 further comprisingthe step of modifying the thin film by ion implantation of apredetermined number of ions/cm².
 45. The method as claimed in claim 28further comprising the step of minimizing bonding between a contactpoint surface of the contact points and the second surface.
 46. Themethod as claimed in claim 45 wherein the step of minimizing the bondingfurther comprises: a. polishing the surfaces to a predetermined degreeof flatness per unit area; b. texturing the surfaces to form a series ofmicroscopic recesses in accordance with a controlled and reproduciblepattern; and c. coating the surfaces with an anti-bonding film.
 47. Themethod as claimed in claim 45 wherein the step of minimizing the bondingfurther comprises: a. limiting a contact pressure between the contactpoint surface and the second surface to be less than 1 MPa; b.controlling the contact point surface and the second surface to have atemperature between 0° C. and 50° C.; c. generating a frequency of therepetitive and alternative expansion and contraction of the firstelement to be in a range between 0 kHz and 120 kHz; and d. selecting thefrequency of the repetitive and alternative expansion and contraction ofthe first element to be a longitudinal acoustic resonant frequency. 48.The method as claimed in claim 45 wherein the step of minimizing thebonding further comprises: a. selecting a melting temperature of asurface material for the second surface to be substantially greater than1000° C.; b. selecting a crystalline structure of the contact pointsurface to be substantially different than a crystalline structure ofthe second surface; and C. selecting a thermal conductivity value of atleast one of the surfaces to be large.
 49. The method as claimed inclaim 28 wherein configuring the contact points further comprises thesteps of: a. determining a root-mean-square velocity of the repetitiveand alterative expansion and contraction of the first element as afunction along the first surface; b. determining a maximumroot-mean-square velocity of the repetitive and alternative expansionand contraction of the first element along the first surface; and c.placing the contact points to a portion of the first surface having theroot-mean-square velocity within a predetermined percentage of themaximum root-mean-square velocity.
 50. The method as claimed in claim 28further comprising the step of initiating a sliding force to at leastone element such that the first element and second element move at atranslational speed relative to one another.
 51. The method as claimedin claim 50 further comprising controlling a root-mean-square velocityof the repetitive and alternative expansion and contraction of the firstelement to be greater than the translational speed between the elements.52. The method as claimed in claim 28 further comprising the step ofcontrolling a cross section of the first element to a predeterminedspecification.
 53. The method as claimed in claim 28 further comprisingthe steps of: a. changing the force; b. generating a signal representingthe change wherein the signal is applied to a feedback mechanism; and c.controlling a cross section along the first element in response to thesignal from the feedback mechanism.
 54. An ultrastiff precision sonicbearing assembly, comprising of: a. at least one load member having aload member mass, each load member having at least one load acceptingsurface and at least one load sliding surface; b. at least one bearingelement having at least one bearing support region and at least onebearing sliding surface; c. the load sliding surface in slidable contactwith the bearing sliding surface by a force, the surfaces in slidablecontact along a slidable path relative to each other; d. the slidingsurfaces having a coefficient of friction therebetween; and e.energizing means for generating a substantially oscillatory slidingmotion in the bearing element, the motion having an oscillation pathtangent with the slidable path for at least one interacting pointbetween the load sliding and the bearing sliding surfaces.
 55. The sonicbearing assembly of claim 54 further comprising: a. the load acceptingsurface being juxtaposed to at least one other, the load acceptingsurface disposed to be oppositely facing the load sliding surface; b.the bearing support region being juxtaposed to at least one other, thebearing support region disposed to be oppositely facing the bearingsliding surface; and c. the force being substantially constant, wherebythe force maintains the sliding contact between the sliding surfaces.56. The sonic bearing assembly of claim 54 wherein the load slidingsurface has a load sliding surface topography, the load sliding surfacetopography is selected from the group consisting of planar, cylindrical,and spherical topographies.
 57. The sonic bearing assembly of claim 56wherein the bearing sliding surface has a bearing sliding surfacetopography, the bearing sliding surface topography complementing theload sliding surface topography.
 58. The sonic bearing assembly of claim54 wherein the load sliding surface has a surface material withpredetermined surface material properties.
 59. The sonic bearingassembly of claim 58 wherein the surface material is selected from thegroup consisting of diamond, diamond-like carbon materials, steelalloys, steel, cubic carbon nitrides, cubic boron nitrides, zirconiumcarbon nitrides, titanium carbon nitrides, titanium aluminum nitrides,aluminum alloys, aluminum, alumina, sapphire, W, Ni, Nb, Ti, Si, Zr, Cr,Hf, Y, oxides of Nb, oxides of Ti, oxides of Si, oxides of Zr, oxides ofCr, oxides of Hf, oxides of Y, carbides of W, carbides of Nb, carbidesof Ti, carbides of Si, carbides of Zr, carbides of Cr, carbides of Ta,carbides of Hf, nitrides of Ti, nitrides of Si, nitrides of B, nitridesof Zr, borides of W, borides of Zr, borides of Ti, borides of Hf,borides of Cr, PTFE polymer, HDPE polymer, and UHMWPE polymer.
 60. Thesonic bearing assembly of claim 54 wherein the bearing sliding surfacehas a surface material with predetermined surface material properties.61. The sonic bearing assembly of claim 60 wherein the surface materialis selected from the group consisting of diamond, diamond like carbonmaterials, steel alloys, steel, cubic carbon nitrides, cubic boronnitrides, zirconium carbon nitrides, titanium carbon nitrides, titaniumaluminum nitrides, aluminum alloys, aluminum, alumina, sapphire, W, Ni,Nb, Ti, Si, Zr, Cr, Hf, Y, oxides of Nb, oxides of Ti, oxides of Si,oxides of Zr, oxides of Cr, oxides of Hf, oxides of Y, carbides of W,carbides of Nb, carbides of Ti, carbides of Si, carbides of Zr, carbidesof Cr, carbides of Ta, carbides of Hf, nitrides of Ti, nitrides of Si,nitrides of B, nitrides of Zr, borides of W, borides of Zr, borides ofTi, borides of Hf, borides of Cr, PTFE polymer, HDPE polymer, and UHMWPEpolymer.
 62. The sonic bearing assembly of claim 58 wherein the surfacematerial is a thin film with a predetermined thickness.
 63. The sonicbearing assembly of claim 62 wherein the thin film is modified by ionimplantation of a predetermined number of ions/cm², whereby the film issubjected to implantation of a depth greater than the thickness of thefilm.
 64. The sonic bearing assembly of claim 60 wherein the surfacematerial is a thin film with a predetermined thickness.
 65. The sonicbearing assembly of claim 64 wherein the thin film is modified by ionimplantation of a predetermined number of ions/cm², whereby the film issubjected to implantation of a depth greater than the thickness of thefilm.
 66. The sonic bearing assembly of claim 54 wherein an actualcoefficient of friction for at least two of the surfaces in slidablecontact are substantially identical and substantially uniform along theslidable path.
 67. The sonic bearing assembly of claim 54 wherein theload member further comprises at least one load guideway member.
 68. Thesonic bearing assembly of claim 67 wherein the load guideway member isattached to the load member by an adhesive means.
 69. The sonic bearingassembly of claim 54 wherein at least one of the bearing element furthercomprises at least one contact pad member having a contact pad surface.70. The sonic bearing assembly of claim 69 wherein the contact padmember is attached to the bearing element by an adhesive means.
 71. Thesonic bearing assembly of claim 69 wherein the contact pad member has apad inertial mass which is substantially smaller than a mass of thebearing element.
 72. The sonic bearing assembly of claim 54 wherein afrequency of the oscillatory sliding motion in the bearing element issubstantially equivalent to an operating frequency of a substantiallylongitudinal acoustic resonant wave, such that a propagation directionof the wave is aligned substantially parallel to the bearing slidingsurface to produce a resonance in the bearing element along thepropagation direction.
 73. The sonic bearing assembly of claim 72wherein the bearing support region is located near a nodal region of thebearing element.
 74. The sonic bearing assembly of claim 54 wherein thebearing element further comprises at least one extension member having:a. an extension member body; and b. a plurality of extension memberfaces, wherein at least one of the extension member faces is anextension attachment face.
 75. The sonic bearing assembly of claim 74wherein the extension member body has a substantially parallelepiped barshape.
 76. The sonic bearing assembly of claim 74 wherein the extensionmember further comprises a horn shape including: a. an input face havingan input surface area; b. an output face having an output surface area;and c. the input surface area being larger than the output surface area.77. The sonic bearing assembly of claim 74 wherein at least one of theextension member faces is the bearing sliding surface.
 78. The sonicbearing assembly of claim 74 wherein the extension member body furthercomprises a material selected from the group consisting of diamond,diamond like carbon materials, piezoelectric materials, magnetostrictivematerials, steel alloys, steel, cubic carbon nitrides, cubic boronnitrides, zirconium carbon nitrides, titanium carbon nitrides, titaniumaluminum nitrides, aluminum alloys, aluminum, alumina, sapphire, W, Ni,Nb, Ti, Si, Zr, Cr, Hf, Y, oxides of Nb, oxides of Ti, oxides of Si,oxides of Zr, oxides of Cr, oxides of Hf, oxides of Y, carbides of W,carbides of Nb, carbides of Ti, carbides of Si, carbides of Zr, carbidesof Cr, carbides of Ta, carbides of Hf, nitrides of Ti, nitrides of Si,nitrides of B, nitrides of Zr, borides of W, borides of Zr, borides ofTi, borides of Hf, borides of Cr, PTFE polymer, HDPE polymer, and UHMWPEpolymer.
 79. The sonic bearing assembly of claim 74 wherein theextension member body has at least one controllable dimension forselecting an operating frequency of a longitudinal acoustic resonantwave therein.
 80. The sonic bearing assembly of claim 79 wherein thecontrollable dimension is adapted to substantially select the operatingfrequency.
 81. The sonic bearing assembly of claim 74 wherein theextension member body has at least one controllable dimension formaximizing an acoustic coupling efficiency to the energizing means for alongitudinal acoustic resonant wave therein.
 82. The sonic bearingassembly of claim 54 wherein the bearing element is comprised of asubstantially bar shaped parallelepiped transducer element including: a.an upper surface; b. a lower surface; and c. a dimension parallel to theupper surface and lower surface.
 83. The sonic bearing assembly of claim82 wherein the transducer element has at least one controllabledimension for selecting a frequency of a longitudinal acoustic resonantwave therein.
 84. The sonic bearing assembly of claim 82 wherein thetransducer element comprises at least one transducer segment having amagnetostrictive material with at least one coil wound around a portionthereof, wherein the coil produces a magnetic field having a magneticfield direction aligned substantially parallel to the dimension of thetransducer element.
 85. The sonic bearing assembly of claim 82 whereinthe transducer element further comprises: a. at least one piezoelectrictransducer having a piezoelectric material; b. the piezoelectrictransducer having an electric dipole moment direction in thepiezoelectric material; c. an upper transducer electrode located on theupper surface of the piezoelectric transducer; d. a lower transducerelectrode located on the lower surface of the piezoelectric transducer;and e. the electrodes disposed perpendicular to the electric dipolemoment direction such that the energizing means produces an electricfield having an electric field direction in the piezoelectric transducersuch that the electric field direction is substantially aligned acrossthe dimension of the transducer.
 86. The sonic bearing assembly of claim85 wherein the transducer element comprises a plurality of piezoelectrictransducers coupled in succession, each having piezoelectric materialproperties.
 87. The sonic bearing assembly of claim 86 wherein theelectric dipole moment direction for one of the plurality of transducersis the same as the electric dipole moment direction for at least oneother of the plurality.
 88. The sonic bearing assembly of claim 86wherein the electric field direction of at least one of the plurality oftransducers is opposite to the electric dipole moment direction ofanother in the plurality.
 89. The sonic bearing assembly of claim 86wherein the electric field direction is opposite to the electric dipolemoment direction.
 90. The sonic bearing assembly of claim 54 furthercomprising a base member, the base member having: a. at least one baseplatform region; and b. at least one base sliding region in slidablecontact with the bearing support region.
 91. The sonic bearing assemblyof claim 90 further comprising at least one contact pad member coupledwith the base sliding region, wherein the contact pad member has acontact pad surface.
 92. The sonic bearing assembly of claim 90 furthercomprising at least one contact pad member coupled with the bearingsupport region, wherein the contact pad member has a contact padsurface.
 93. The sonic bearing assembly of claim 90 further comprising:a. at least one contact pad member coupled with the base sliding region,wherein the contact pad member has a contact pad surface; and b. atleast one contact pad member coupled with the bearing support region,wherein the contact pad member has a contact pad surface, whereby thebase sliding region contact pad surface and the bearing support regioncontact pad surface are in slidable contact with one another.
 94. Thesonic bearing assembly of claim 90 wherein the base platform region isjuxtaposed to another, the base platform region disposed to beoppositely facing the base sliding region.
 95. The sonic bearingassembly of claim 90 wherein the base sliding region has a base slidingregion topography, the base sliding region topography is selected fromthe group consisting of planar, cylindrical, and spherical topographies.96. The sonic bearing assembly of claim 95 wherein the bearing supportregion has a bearing support region topography, the bearing supportregion topography complementing the topography of the base slidingregion.
 97. The sonic bearing assembly of claim 90 wherein the basesliding region has a surface material of predetermined surface materialproperties.
 98. The sonic bearing assembly of claim 97 wherein thesurface material is a thin film with a predetermined thickness.
 99. Thesonic bearing assembly of claim 98 wherein the thin film is modified byion implantation of a predetermined number of ions/cm², whereby the filmis subjected to implantation of a depth greater than the thickness ofthe film .
 100. The sonic bearing assembly of claim 97 wherein thesurface material is selected from the group consisting of diamond,diamond like carbon materials, steel alloys, steel, cubic carbonnitrides, cubic boron nitrides, zirconium carbon nitrides, titaniumcarbon nitrides, titanium aluminum nitrides, aluminum alloys, aluminum,alumina, sapphire, W, Ni, Nb, Ti, Si, Zr, Cr, Hf, Y, oxides of Nb,oxides of Ti, oxides of Si, oxides of Zr, oxides of Cr, oxides of Hf,oxides of Y, carbides of W, carbides of Nb, carbides of Ti, carbides ofSi, carbides of Zr, carbides of Cr, carbides of Ta, carbides of Hf,nitrides of Ti, nitrides of Si, nitrides of B, nitrides of Zr, boridesof W, borides of Zr, borides of Ti, borides of Hf, borides of Cr, PTFEpolymer, HDPE polymer, and UHMWPE polymer.
 101. The sonic bearingassembly of claim 90 wherein an actual coefficient of friction for atleast two of the surfaces in slidable contact are substantiallyidentical and substantially uniform along the slidable path.
 102. Thesonic bearing assembly of claim 90 wherein the base member furthercomprises a piezoelectric transducer element.
 103. The sonic bearingassembly of claim 90 wherein the base member further comprises amagnetostrictive transducer element.
 104. The sonic bearing assembly ofclaim 90 wherein the base member further comprises at least one supportmember region disposed in the base sliding region.
 105. The sonicbearing assembly of claim 104 further comprising at least one supportmember, the support member being attached between the bearing supportregion and the support member region by an adhesive means.
 106. Thesonic bearing assembly of claim 105 wherein the support member iscomprised of a piezoelectric transducer element.
 107. The sonic bearingassembly of claim 105 wherein the support member is comprised of amagnetostrictive transducer element.
 108. The sonic bearing assembly ofclaim 105 wherein the support member is comprised of an insulatormaterial.
 109. The sonic bearing assembly of claim 54 further comprisinga lubricant disposed on any of the sliding surfaces.
 110. The sonicbearing assembly of claim 109 wherein the lubricant is selected from thegroup consisting of molybdenum disulfide, mineral oil, saponified oils,greases, and any combination thereof.
 111. The sonic bearing assembly ofclaim 109 wherein the lubricant is contained within a cavity of areservoir structure, the reservoir structure attached to the bearingassembly.
 112. The sonic bearing assembly of claim 54 wherein theenergizing means comprises at least one excitation driver.
 113. Thesonic bearing assembly of claim 112 wherein at least a portion of theexcitation driver is contained within an electronics package.
 114. Thesonic bearing assembly of claim 54 further including a controlling meansfor controlling a root-mean-square velocity of the oscillatory slidingmotion.
 115. The sonic bearing assembly of claim 114 wherein at least aportion of the controlling means is contained within an electronicspackage.
 116. The sonic bearing assembly of claim 54 further comprisinga controlling means for controlling a cross section of the bearingelement.
 117. The sonic bearing assembly of claim 116 wherein at least aportion of the controlling means is contained within an electronicspackage.
 118. The sonic bearing assembly of claim 54 further comprisinga bias means for altering a dimension of the bearing element.
 119. Thesonic bearing assembly of claim 118 wherein at least a portion of thebias means is contained within an electronics package.
 120. The sonicbearing assembly of claim 54 further comprising a sensing means fordetermining a magnitude of the force, wherein the force is normal to thebearing element.
 121. The sonic bearing assembly of claim 120 whereinthe sensing means generates a signal for representing the magnitude ofthe force.
 122. The sonic bearing assembly of claim 120 wherein thesensing means further comprises a sensor for measuring a value forfrictional power dissipation.
 123. The sonic bearing assembly of claim120 wherein the sensor is contained within at least a portion of thebearing element.
 124. The sonic bearing assembly of claim 54 furthercomprising a controlling means for minimizing bonding between thesliding surfaces.
 125. An ultrastiff sonic bearing assembly, comprising:a. at least one load member having at least one load sliding surface; b.at least one base member having at least one base sliding region; c. atleast one bearing element further comprising: i. a bearing body having avariable static stiffness and a variable dynamic stiffness; ii. abearing sliding surface, the bearing sliding surface in continuousslidable contact with the load sliding surface by a force for slidingalong any slidable path; iii. a bearing support region disposed incontact with the base sliding region by the force; d. energizing meansfor converting electrical energy into microscopic mechanicaldisplacement in the bearing element, the displacement for inducing asubstantially oscillatory sliding motion, having an oscillation pathalong any slidable path; and e. a stiffness altering means forcontrolling the static and dynamic stiffness characteristics of thebearing assembly.
 126. The sonic bearing assembly of claim 125 whereinthe stiffness altering means is comprised of at least one force servomechanism for maintaining a constant stiffness throughout the bearingassembly.
 127. The sonic bearing assembly of claim 126 wherein at leasta portion of the force servo mechanism is contained within anelectronics package.
 128. The sonic bearing assembly of claim 126wherein the force servo mechanism further comprises a sensing means fordetermining a change in magnitude of the force.
 129. The sonic bearingassembly of claim 128 wherein the sensing means generates a force outputsignal representing the magnitude.
 130. The sonic bearing assembly ofclaim 129 further including a controlling means for controlling a crosssection of the bearing element to a predetermined specification. 131.The sonic bearing assembly of claim 130 wherein a portion of thecontrolling means compares the force output signal with a referencelevel representing the predetermined specification.
 132. A method ofcontrolling an effective coefficient of friction between a first surfaceof a first element and a second surface of a second element, the methodcomprising the steps of: a. providing a contact point on the firstsurface; b. configuring the contact point and the second surface to bein slidable contact with one another along an interface and under aforce sufficient to maintain contact and having a static frictiontherebetween; c. energizing the first element to produce a repetitivemotion of the contact point such that the effective coefficient offriction is altered; and d. determining a change in applied powerrequired for producing the motion as a result of a variation in theforce.
 133. The method as claimed in claim 132 wherein the first elementfurther comprises at least one transducer for converting electricalenergy into microscopic mechanical displacement.
 134. The method asclaimed in claim 133 further including the step of utilizing anexcitation means for generating the electrical energy.
 135. The methodas claimed in claim 132 further including the step of controlling aroot-mean-square velocity of the motion at a predeterminedspecification.
 136. The method as claimed in claim 132 wherein the stepof determining the change in applied power comprises: a. determining aninitial level of the applied power required for inducing the motionbefore the variation; b. determining a final level of the applied powerrequired for inducing the motion after the variation; and c. calculatinga difference between the final level and the initial level.
 137. Themethod as claimed in claim 132 further including the step of generatinga signal which represents the variation in the force, the signal beingapplied to an output device.
 138. The method as claimed in claim 137wherein the output device is a feedback mechanism.
 139. The method asclaimed in claim 132 further comprising a step of suppressing aplurality of side effects, wherein the side effects further comprisebond formation between the contact point and second surface thatprevents relative movement therebetween.
 140. The method as claimed inclaim 132 further comprising a step of suppressing a plurality of sideeffects, wherein the side effects further comprise at least onetranslational force in-between the surfaces.